(i dont remember exactly if it was 8032038 or some other number, so correct me on this)
(i posted this at 12:29) lol
?
?
Y by
What is the value of 
This post has been edited 2 times. Last edited by fruitmonster97, Nov 7, 2024, 5:39 PM
G
Topic
First Poster
Last Poster
k a April Highlights and 2025 AoPS Online Class Information
jlacosta 0
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.
WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.
Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!
Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Introductory: Grades 5-10
Prealgebra 1 Self-Paced
Prealgebra 1
Sunday, Apr 13 - Aug 10
Tuesday, May 13 - Aug 26
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Sunday, Jun 15 - Oct 12
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Wednesday, Jul 16 - Oct 29
Prealgebra 2 Self-Paced
Prealgebra 2
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Friday, Jul 25 - Nov 21
Introduction to Algebra A Self-Paced
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Introduction to Counting & Probability Self-Paced
Introduction to Counting & Probability
Wednesday, Apr 16 - Jul 2
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Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19
Introduction to Number Theory
Thursday, Apr 17 - Jul 3
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Monday, Jun 9 - Aug 25
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Tuesday, Jul 15 - Sep 30
Introduction to Algebra B Self-Paced
Introduction to Algebra B
Wednesday, Apr 16 - Jul 30
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Friday, Jul 18 - Nov 14
Introduction to Geometry
Wednesday, Apr 23 - Oct 1
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Intermediate: Grades 8-12
Intermediate Algebra
Monday, Apr 21 - Oct 13
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Wednesday, Jun 25 - Dec 10
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Thursday, Jul 24 - Jan 22
Intermediate Counting & Probability
Wednesday, May 21 - Sep 17
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Intermediate Number Theory
Friday, Apr 11 - Jun 27
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Precalculus
Wednesday, Apr 9 - Sep 3
Friday, May 16 - Oct 24
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Monday, Jun 30 - Dec 8
Advanced: Grades 9-12
Olympiad Geometry
Tuesday, Jun 10 - Aug 26
Calculus
Tuesday, May 27 - Nov 11
Wednesday, Jun 25 - Dec 17
Group Theory
Thursday, Jun 12 - Sep 11
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Wednesday, Apr 16 - Jul 2
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
MATHCOUNTS/AMC 8 Advanced
Friday, Apr 11 - Jun 27
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21
AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22
AMC 12 Final Fives
Sunday, May 18 - Jun 15
F=ma Problem Series
Wednesday, Jun 11 - Aug 27
WOOT Programs
Visit the pages linked for full schedule details for each of these programs!
MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT
Programming
Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
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Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
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Tuesday, May 13 - Jul 29
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Physics
Introduction to Physics
Wednesday, May 21 - Aug 6
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Monday, Jun 23 - Sep 15
Physics 1: Mechanics
Thursday, May 22 - Oct 30
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Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)
WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.
Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!
Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Introductory: Grades 5-10
Prealgebra 1 Self-Paced
Prealgebra 1
Sunday, Apr 13 - Aug 10
Tuesday, May 13 - Aug 26
Thursday, May 29 - Sep 11
Sunday, Jun 15 - Oct 12
Monday, Jun 30 - Oct 20
Wednesday, Jul 16 - Oct 29
Prealgebra 2 Self-Paced
Prealgebra 2
Sunday, Apr 13 - Aug 10
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Introduction to Algebra A Self-Paced
Introduction to Algebra A
Monday, Apr 7 - Jul 28
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Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
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Tuesday, Jul 15 - Oct 28
Introduction to Counting & Probability Self-Paced
Introduction to Counting & Probability
Wednesday, Apr 16 - Jul 2
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19
Introduction to Number Theory
Thursday, Apr 17 - Jul 3
Friday, May 9 - Aug 1
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Tuesday, Jul 15 - Sep 30
Introduction to Algebra B Self-Paced
Introduction to Algebra B
Wednesday, Apr 16 - Jul 30
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Introduction to Geometry
Wednesday, Apr 23 - Oct 1
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Monday, Jul 14 - Jan 19
Intermediate: Grades 8-12
Intermediate Algebra
Monday, Apr 21 - Oct 13
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22
Intermediate Counting & Probability
Wednesday, May 21 - Sep 17
Sunday, Jun 22 - Nov 2
Intermediate Number Theory
Friday, Apr 11 - Jun 27
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3
Precalculus
Wednesday, Apr 9 - Sep 3
Friday, May 16 - Oct 24
Sunday, Jun 1 - Nov 9
Monday, Jun 30 - Dec 8
Advanced: Grades 9-12
Olympiad Geometry
Tuesday, Jun 10 - Aug 26
Calculus
Tuesday, May 27 - Nov 11
Wednesday, Jun 25 - Dec 17
Group Theory
Thursday, Jun 12 - Sep 11
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Wednesday, Apr 16 - Jul 2
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
MATHCOUNTS/AMC 8 Advanced
Friday, Apr 11 - Jun 27
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21
AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22
AMC 12 Final Fives
Sunday, May 18 - Jun 15
F=ma Problem Series
Wednesday, Jun 11 - Aug 27
WOOT Programs
Visit the pages linked for full schedule details for each of these programs!
MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT
Programming
Introduction to Programming with Python
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Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22
Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
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USACO Bronze Problem Series
Tuesday, May 13 - Jul 29
Sunday, Jun 22 - Sep 1
Physics
Introduction to Physics
Wednesday, May 21 - Aug 6
Sunday, Jun 15 - Sep 14
Monday, Jun 23 - Sep 15
Physics 1: Mechanics
Thursday, May 22 - Oct 30
Monday, Jun 23 - Dec 15
Relativity
Sat & Sun, Apr 26 - Apr 27 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)
0 replies
k i Adding contests to the Contest Collections
dcouchman 1
N
by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.
Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
k i Zero tolerance
ZetaX 49
N
by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:
To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.
More specifically:
For new threads:
a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.
Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"
b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.
Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".
c) Good problem statement:
Some recent really bad post was:
[quote]
[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.
For answers to already existing threads:
d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve
, do not answer with "
is a solution" only. Either you post any kind of proof or at least something unexpected (like "
is the smallest solution). Someone that does not see that is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.
e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.
To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!
Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).
The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
But please follow the following guideline:
To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.
More specifically:
For new threads:
a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.
Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"
b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.
Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".
c) Good problem statement:
Some recent really bad post was:
[quote]
[/quote]It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.
For answers to already existing threads:
d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve
, do not answer with "
is a solution" only. Either you post any kind of proof or at least something unexpected (like "
is the smallest solution). Someone that does not see that is a solution of the above without your post is completely wrong here, this is an IMO-level forum.Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.
e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.
To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!
Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).
The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
Discuss the Stanford Math Tournament Here
Aaronjudgeisgoat 251
N
by Shreyasharma
I believe discussion is allowed after yesterday at midnight, correct?
If so, I will put tentative answers on this thread.
By the way, does anyone know the answer to Geometry Problem 5? I was wondering if I got that one right
Also, if you put answers, please put it in a hide tag
If so, I will put tentative answers on this thread.
By the way, does anyone know the answer to Geometry Problem 5? I was wondering if I got that one right
Also, if you put answers, please put it in a hide tag
251 replies
NYMC High School Summer Program (HSSP)
missionsqhc 0
I was recently accepted into the black level of New York Math Circle's High School Summer Program (HSSP). I would be taking this program as a prefrosh and wondering if anyone who has experience with this program could comment on it. It's my understanding that the program will heavily focus on problem solving and competitions rather than math research. In that case, would it offer any benefit to an incoming college math major?
0 replies
Hard Polynomial Problem
MinhDucDangCHL2000 1
N
by Tung-CHL
Source: IDK
Let 
be a polynomial with integer coefficients. Suppose there exist infinitely many integer pairs 
such that 
. Prove that the graph of is symmetric about a point (i.e., it has a center of symmetry).
be a polynomial with integer coefficients. Suppose there exist infinitely many integer pairs 
such that 
. Prove that the graph of is symmetric about a point (i.e., it has a center of symmetry).1 reply
IMO LongList 1985 CYP2 - System of Simultaneous Equations
Amir Hossein 13
N
by cubres
Solve the system of simultaneous equations
![\[\sqrt x - \frac 1y - 2w + 3z = 1,\]](//latex.artofproblemsolving.com/d/0/f/d0ff4819db851e6c12f738dcdb6b81bbd2ed0ca7.png)
![\[x + \frac{1}{y^2} - 4w^2 - 9z^2 = 3,\]](//latex.artofproblemsolving.com/6/5/3/653c1547620f85ff761817a5cc333f16bce9c4c6.png)
![\[x \sqrt x - \frac{1}{y^3} - 8w^3 + 27z^3 = -5,\]](//latex.artofproblemsolving.com/1/b/9/1b9c2ed383acc931aa3607ba82031e182e18f3d1.png)
![\[x^2 + \frac{1}{y^4} - 16w^4 - 81z^4 = 15.\]](//latex.artofproblemsolving.com/e/0/3/e032ce109cd74bbae47dc6bca04dcab2d8f9ef29.png)
![\[\sqrt x - \frac 1y - 2w + 3z = 1,\]](http://latex.artofproblemsolving.com/d/0/f/d0ff4819db851e6c12f738dcdb6b81bbd2ed0ca7.png)
![\[x + \frac{1}{y^2} - 4w^2 - 9z^2 = 3,\]](http://latex.artofproblemsolving.com/6/5/3/653c1547620f85ff761817a5cc333f16bce9c4c6.png)
![\[x \sqrt x - \frac{1}{y^3} - 8w^3 + 27z^3 = -5,\]](http://latex.artofproblemsolving.com/1/b/9/1b9c2ed383acc931aa3607ba82031e182e18f3d1.png)
![\[x^2 + \frac{1}{y^4} - 16w^4 - 81z^4 = 15.\]](http://latex.artofproblemsolving.com/e/0/3/e032ce109cd74bbae47dc6bca04dcab2d8f9ef29.png)
13 replies
Tennessee Math Tournament (TMT) Online 2025
TennesseeMathTournament 72
N
by Ruegerbyrd
Hello everyone! We are excited to announce a new competition, the Tennessee Math Tournament, created by the Tennessee Math Coalition! Anyone can participate in the virtual competition for free.
The testing window is from March 22nd to April 12th, 2025. Virtual competitors may participate in the competition at any time during that window.
The virtual competition consists of three rounds: Individual, Bullet, and Team. The Individual Round is 60 minutes long and consists of 30 questions (AMC 10 level). The Bullet Round is 20 minutes long and consists of 80 questions (Mathcounts Chapter level). The Team Round is 30 minutes long and consists of 16 questions (AMC 12 level). Virtual competitors may compete in teams of four, or choose to not participate in the team round.
To register and see more information, click here!
If you have any questions, please email connect@tnmathcoalition.org or reply to this thread!
Thank you to our lead sponsor, Jane Street!
IMAGE
The testing window is from March 22nd to April 12th, 2025. Virtual competitors may participate in the competition at any time during that window.
The virtual competition consists of three rounds: Individual, Bullet, and Team. The Individual Round is 60 minutes long and consists of 30 questions (AMC 10 level). The Bullet Round is 20 minutes long and consists of 80 questions (Mathcounts Chapter level). The Team Round is 30 minutes long and consists of 16 questions (AMC 12 level). Virtual competitors may compete in teams of four, or choose to not participate in the team round.
To register and see more information, click here!
If you have any questions, please email connect@tnmathcoalition.org or reply to this thread!
Thank you to our lead sponsor, Jane Street!
IMAGE
72 replies
Centroid Distance Identity in Triangle
zeta1 5
N
by DottedCaculator
Let M be any point inside triangle ABC, and let G be the centroid of triangle ABC. Prove that:
![\[
|MA|^2 + |MB|^2 + |MC|^2 = |GA|^2 + |GB|^2 + |GC|^2 + 3|MG|^2
\]](//latex.artofproblemsolving.com/0/7/0/070ff15920d19d474defb77ceb606b2811fa85b4.png)
![\[
|MA|^2 + |MB|^2 + |MC|^2 = |GA|^2 + |GB|^2 + |GC|^2 + 3|MG|^2
\]](http://latex.artofproblemsolving.com/0/7/0/070ff15920d19d474defb77ceb606b2811fa85b4.png)
5 replies
Numbers not power of 5
Kayak 34
N
by cursed_tangent1434
Source: Indian TST D1 P2
Show that there do not exist natural numbers 
such that the numbers ![\[ (a_1)^{2018}+a_2, (a_2)^{2018}+a_3, \dots, (a_{2018})^{2018}+a_1 \]](//latex.artofproblemsolving.com/6/1/a/61ad92b49bd9b4b8839e6f6c4e81c758a11835a3.png)
are all powers of 
Proposed by Tejaswi Navilarekallu
such that the numbers ![\[ (a_1)^{2018}+a_2, (a_2)^{2018}+a_3, \dots, (a_{2018})^{2018}+a_1 \]](http://latex.artofproblemsolving.com/6/1/a/61ad92b49bd9b4b8839e6f6c4e81c758a11835a3.png)
are all powers of 
Proposed by Tejaswi Navilarekallu
34 replies
9 Which math contest is your favorite?
mdk2013 84
N
by Pengu14
i think thats all the major ones, comment if you have any more that i forgot to include
upvote if you're like me and you think MATHCOUNTS is obv better!
EDIT: i forgot ARML and JBMO, comment if you like those
84 replies
Number Theory Chain!
JetFire008 58
N
by Primeniyazidayi
I will post a question and someone has to answer it. Then they have to post a question and someone else will answer it and so on. We can only post questions related to Number Theory and each problem should be more difficult than the previous. Let's start!
58 replies
Silly Sequences
whatshisbucket 25
N
by bin_sherlo
Source: ELMO 2018 #2, 2018 ELMO SL N3
Consider infinite sequences 
of positive integers satisfying 
and 
for all positive integers 
and 
For a given positive integer 
find the maximum possible value of 
Proposed by Krit Boonsiriseth
of positive integers satisfying 
and 
for all positive integers 
and 
For a given positive integer 
find the maximum possible value of 
Proposed by Krit Boonsiriseth
25 replies
Advanced topics in Inequalities
va2010 8
N
by sqing
So a while ago, I compiled some tricks on inequalities. You are welcome to post solutions below!
8 replies
Divisibility NT FE
CHESSR1DER 12
N
by internationalnick123456
Source: Own
Find all functions 
such for any 
:
.
such for any 
:
.
12 replies
Let \( a_1, a_2, \dots, a_n \) and \( b_1, b_2, \dots, b_n \) be nonzero real nu
Jackson0423 0
Let 
and 
be nonzero real numbers satisfying
![\[
a_1^2 b_1^2 (a_1 + b_1) + a_2^2 b_2^2 (a_2 + b_2) + \cdots + a_n^2 b_n^2 (a_n + b_n) \leq 7,
\]](//latex.artofproblemsolving.com/a/7/e/a7ea7af24ac529090f3b2e305be43e2728b79eb4.png)
![\[
\frac{1}{a_1} + \cdots + \frac{1}{a_n} = \frac{1}{4}, \quad \frac{1}{b_1} + \cdots + \frac{1}{b_n} = \frac{1}{3}.
\]](//latex.artofproblemsolving.com/e/f/3/ef341b850979a9b780f5daaa49f46f1d1324cdbd.png)
Find the maximum value of
![\[
a_1 b_1 + a_2 b_2 + \cdots + a_n b_n.
\]](//latex.artofproblemsolving.com/d/3/3/d338bf5be4f1a218e150bfd84173e988ee92ddad.png)
and 
be nonzero real numbers satisfying![\[
a_1^2 b_1^2 (a_1 + b_1) + a_2^2 b_2^2 (a_2 + b_2) + \cdots + a_n^2 b_n^2 (a_n + b_n) \leq 7,
\]](http://latex.artofproblemsolving.com/a/7/e/a7ea7af24ac529090f3b2e305be43e2728b79eb4.png)
![\[
\frac{1}{a_1} + \cdots + \frac{1}{a_n} = \frac{1}{4}, \quad \frac{1}{b_1} + \cdots + \frac{1}{b_n} = \frac{1}{3}.
\]](http://latex.artofproblemsolving.com/e/f/3/ef341b850979a9b780f5daaa49f46f1d1324cdbd.png)
Find the maximum value of![\[
a_1 b_1 + a_2 b_2 + \cdots + a_n b_n.
\]](http://latex.artofproblemsolving.com/d/3/3/d338bf5be4f1a218e150bfd84173e988ee92ddad.png)
0 replies
Let \[ P(x) = a_0 + a_1 x^2 + a_2 x^4 + \cdots + a_{10} x^{20} \] be a polynom
Jackson0423 0
Let
![\[
P(x) = a_0 + a_1 x^2 + a_2 x^4 + \cdots + a_{10} x^{20}
\]](//latex.artofproblemsolving.com/0/d/c/0dcd08456f253de08f3b880c7a1fddc07b335932.png)
be a polynomial of degree 20 with only even powers of 
.
Let the roots of
be 
.
Given that
![\[
(x_1^2 + 1)(x_2^2 + 1) \cdots (x_{20}^2 + 1) = 2025,
\]](//latex.artofproblemsolving.com/b/a/4/ba4bc5f526565e56a9a685fe01572c1366241084.png)
find the **minimum value** of 
.
``
![\[
P(x) = a_0 + a_1 x^2 + a_2 x^4 + \cdots + a_{10} x^{20}
\]](http://latex.artofproblemsolving.com/0/d/c/0dcd08456f253de08f3b880c7a1fddc07b335932.png)
be a polynomial of degree 20 with only even powers of 
.Let the roots of
be 
.Given that
![\[
(x_1^2 + 1)(x_2^2 + 1) \cdots (x_{20}^2 + 1) = 2025,
\]](http://latex.artofproblemsolving.com/b/a/4/ba4bc5f526565e56a9a685fe01572c1366241084.png)
find the **minimum value** of 
.``
0 replies
five digit multiplication?
G
H
G
H
Source: 2024 AMC 10A #1/AMC 12A #1
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Z
K
Y
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#6
Nov 7, 2024, 4:44 PM
Y by
this is actually kinda hard for #1 lol
the answer is A, notice
and the left two multiplications are equal
the answer is A, notice
and the left two multiplications are equal
Z
K
Y
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and 
,
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Y by TheEmperorPenguin
bruh spent 6 minutes doing this one and checking > : (
Z
K
Y
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and 
so our answer is 
answer choice 
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K
Y
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Y by Nobitasolvesproblems1979
i got 21 somehow :skull: don't question it
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Y
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#14
Nov 7, 2024, 4:51 PM
Y by
i did some weird substitution but just look and you can see it has to end with a 2 so A is the only choice
Z
K
Y
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also ends in 
.
.
,
.
,
or 
G
H
