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k a April Highlights and 2025 AoPS Online Class Information
jlacosta 0
Apr 2, 2025
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
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
Wednesday, May 7 - Aug 20
Monday, Jun 2 - Sep 22
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Friday, Jul 25 - Nov 21
Introduction to Algebra A Self-Paced
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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
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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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Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30
Introduction to Algebra B Self-Paced
Introduction to Algebra B
Wednesday, Apr 16 - Jul 30
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14
Introduction to Geometry
Wednesday, Apr 23 - Oct 1
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
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Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
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
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Calculus
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Thursday, Jun 12 - Sep 11
Contest Preparation: Grades 6-12
MATHCOUNTS/AMC 8 Basics
Wednesday, Apr 16 - Jul 2
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Monday, Jun 2 - Aug 18
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Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
MATHCOUNTS/AMC 8 Advanced
Friday, Apr 11 - Jun 27
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Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
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Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
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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
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Sunday, May 18 - Jun 15
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Wednesday, Jun 11 - Aug 27
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Visit the pages linked for full schedule details for each of these programs!
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Intermediate Programming with Python
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Introduction to Physics
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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!)
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
Wednesday, May 7 - Aug 20
Monday, Jun 2 - Sep 22
Sunday, Jun 29 - Oct 26
Friday, Jul 25 - Nov 21
Introduction to Algebra A Self-Paced
Introduction to Algebra A
Monday, Apr 7 - Jul 28
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
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
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Tuesday, Jul 15 - Sep 30
Introduction to Algebra B Self-Paced
Introduction to Algebra B
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Friday, Jul 18 - Nov 14
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
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
Monday, Jun 30 - Sep 22
Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
Monday, Jun 30 - Sep 22
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
Apr 5, 2023
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
May 4, 2019
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]

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




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
Advanced topics in Inequalities
va2010 18
N
a minute ago
by sqing
So a while ago, I compiled some tricks on inequalities. You are welcome to post solutions below!
18 replies

two subsets with no fewer than four common elements.
micliva 39
N
24 minutes ago
by de-Kirschbaum
Source: All-Russian Olympiad 1996, Grade 9, First Day, Problem 4
In the Duma there are 1600 delegates, who have formed 16000 committees of 80 persons each. Prove that one can find two committees having no fewer than four common members.
A. Skopenkov
A. Skopenkov
39 replies
3 knightlike moves is enough
sarjinius 2
N
25 minutes ago
by cooljoseph
Source: Philippine Mathematical Olympiad 2025 P6
An ant is on the Cartesian plane. In a single move, the ant selects a positive integer
, then either travels [list]
[*]
units vertically (up or down) and
units horizontally (left or right); or
[*]
units horizontally (left or right) and
units vertically (up or down).
[/list]
Thus, for any
, the ant can choose to go to one of eight possible points.
Prove that, for any integers
and
, the ant can travel from
to
using at most
moves.

[*]


[*]


[/list]
Thus, for any

Prove that, for any integers





2 replies
16th ibmo - uruguay 2001/q3.
carlosbr 21
N
35 minutes ago
by de-Kirschbaum
Source: Spanish Communities
Let
be a set of
elements and
are subsets of
(
), such that every one of them has at least
elements.
Show that there exists
and
, with
, such that the number of common elements of
and
is greater or equal to:






Show that there exists






21 replies

Weird Geo
Anto0110 1
N
41 minutes ago
by cooljoseph
In a trapezium
, the sides
and
are parallel and the angles
and
are acute. Show that it is possible to divide the triangle
into 4 disjoint triangle
and the triangle
into 4 disjoint triangles
such that the triangles
and
are congruent for all
.












1 reply

Dear Sqing: So Many Inequalities...
hashtagmath 35
N
2 hours ago
by ohiorizzler1434
I have noticed thousands upon thousands of inequalities that you have posted to HSO and was wondering where you get the inspiration, imagination, and even the validation that such inequalities are true? Also, what do you find particularly appealing and important about specifically inequalities rather than other branches of mathematics? Thank you :)
35 replies
1 viewing
Maximum of Incenter-triangle
mpcnotnpc 4
N
2 hours ago
by mpcnotnpc
Triangle
has side lengths
,
, and
. Select a point
inside
, and construct the incenters of
,
, and
and denote them as
,
,
. What is the maximum area of the triangle
?













4 replies
Something nice
KhuongTrang 26
N
2 hours ago
by KhuongTrang
Source: own
Problem. Given
be non-negative real numbers such that
Prove that



26 replies
Tiling rectangle with smaller rectangles.
MarkBcc168 59
N
3 hours ago
by Bonime
Source: IMO Shortlist 2017 C1
A rectangle
with odd integer side lengths is divided into small rectangles with integer side lengths. Prove that there is at least one among the small rectangles whose distances from the four sides of
are either all odd or all even.
Proposed by Jeck Lim, Singapore


Proposed by Jeck Lim, Singapore
59 replies
Existence of AP of interesting integers
DVDthe1st 34
N
4 hours ago
by DeathIsAwe
Source: 2018 China TST Day 1 Q2
A number
is interesting if 2018 divides
(the number of positive divisors of
). Determine all positive integers
such that there exists an infinite arithmetic progression with common difference
whose terms are all interesting.





34 replies
Strange Geometry
Itoz 1
N
4 hours ago
by hukilau17
Source: Own
Given a fixed circle
with its center
. There are two fixed points
and one moving point
on
. The midpoint of the line segment
is
.
is a fixed point on
. Line
intersects
at
, and line
intersects
at
.
Find all the fixed points
such that
is always tangent to
when
varies.
Hint















Find all the fixed points




Hint
Consider the two midpoints of arc
.

1 reply
find all pairs of positive integers
Khalifakhalifa 2
N
5 hours ago
by Haris1
Find all pairs of positive integers

![\[
a^2 + b^2 \mid a^3 + b^3
\]](http://latex.artofproblemsolving.com/a/1/d/a1ddbd20c854e291da5670de449229d1664fa56c.png)
2 replies
D860 : Flower domino and unconnected
Dattier 4
N
5 hours ago
by Haris1
Source: les dattes à Dattier
Let G be a grid of size m*n.
We have 2 dominoes in flowers and not connected like here
IMAGE
Determine a necessary and sufficient condition on m and n, so that G can be covered with these 2 kinds of dominoes.
We have 2 dominoes in flowers and not connected like here
IMAGE
Determine a necessary and sufficient condition on m and n, so that G can be covered with these 2 kinds of dominoes.
4 replies

hard problem
G
H
J
G
H
BBookmark
kLocked
kLocked
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Y by PikaPika999
ND_ wrote:
When is equality achieved? a=b=c doesn't satisfy the initial condition. I think minimum is 10.
with equality occurring when

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Y by PikaPika999
I used Cauchy and got
so i think 10 is the min, and I dont think 9 is achievable.

Z
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Y by xytunghoanh, PikaPika999
xytunghoanh wrote:
Cobedangiu wrote:
problem

cmath?
Z
K
Y
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Y by PikaPika999
I can help you to solve this. Check pm for Vietnamese solution.
Z
K
Y
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Y by xytunghoanh, PikaPika999
xytunghoanh wrote:
I can help you to solve this. Check pm for Vietnamese solution.
This post has been edited 1 time. Last edited by Cobedangiu, Mar 27, 2025, 5:27 PM
Z
K
Y
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Y by PikaPika999
Cobedangiu wrote:
problem




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Y
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Y by Maximilian113, PikaPika999
k this is SUPER hard
why is inequality not satisfied by a=b=c?
suggests something funny like calculus
edit: ok im back with a fake solve!!!!!!!
Solve:
Expand
to get
into which we now substitute
.
this now gives us
which taking the double derivative gives that this function is convex.
so we can apply Karamata (smoothing kind of) to give us that equality case is where two of
are equal and consequently two of
equal.
note that scaling doesn't change anything in the inequality so you homogenize by setting idk
and then going back into the condition
we should get
must be the minimum and consequently the minimum value is achieved at 10????????????
why is inequality not satisfied by a=b=c?
suggests something funny like calculus
edit: ok im back with a fake solve!!!!!!!
Solve:
Expand



this now gives us

so we can apply Karamata (smoothing kind of) to give us that equality case is where two of


note that scaling doesn't change anything in the inequality so you homogenize by setting idk


we should get

This post has been edited 1 time. Last edited by InftyByond, Apr 6, 2025, 5:34 AM
Reason: fake proof issues die hard
Reason: fake proof issues die hard
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K
Y
The post below has been deleted. Click to close.
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Y by PikaPika999
InftyByond wrote:
k this is SUPER hard
why is inequality not satisfied by a=b=c?
suggests something funny like calculus
edit: ok im back with a fake solve!!!!!!!
Solve:
Expand
to get
into which we now substitute
.
this now gives us
which taking the double derivative gives that this function is convex.
so we can apply Karamata (smoothing kind of) to give us that equality case is where two of
are equal and consequently two of
equal.
note that scaling doesn't change anything in the inequality so you homogenize by setting idk
and then going back into the condition
we should get
must be the minimum and consequently the minimum value is achieved at 10????????????
why is inequality not satisfied by a=b=c?
suggests something funny like calculus
edit: ok im back with a fake solve!!!!!!!
Solve:
Expand



this now gives us

so we can apply Karamata (smoothing kind of) to give us that equality case is where two of


note that scaling doesn't change anything in the inequality so you homogenize by setting idk


we should get

The problem has been solved


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K
Y
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Y by PikaPika999, anduran, truongphatt2668
Cobedangiu wrote:
problem

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K
Y
The post below has been deleted. Click to close.
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Y by PikaPika999
Cobedangiu wrote:
InftyByond wrote:
k this is SUPER hard
why is inequality not satisfied by a=b=c?
suggests something funny like calculus
edit: ok im back with a fake solve!!!!!!!
Solve:
Expand
to get
into which we now substitute
.
this now gives us
which taking the double derivative gives that this function is convex.
so we can apply Karamata (smoothing kind of) to give us that equality case is where two of
are equal and consequently two of
equal.
note that scaling doesn't change anything in the inequality so you homogenize by setting idk
and then going back into the condition
we should get
must be the minimum and consequently the minimum value is achieved at 10????????????
why is inequality not satisfied by a=b=c?
suggests something funny like calculus
edit: ok im back with a fake solve!!!!!!!
Solve:
Expand



this now gives us

so we can apply Karamata (smoothing kind of) to give us that equality case is where two of


note that scaling doesn't change anything in the inequality so you homogenize by setting idk


we should get

The problem has been solved


K so i looked at the solve
Its pretty nice and slick with no calculus
Is my alternate solve wrong then? not surprised
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Y by
See this https://artofproblemsolving.com/community/c6h1834400p23632179 for more information
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