Stay ahead of learning milestones! Enroll in a class over the summer!

G
Topic
First Poster
Last Poster
k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. 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 upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/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
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
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
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
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
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
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
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14

Introduction to Geometry
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19

Paradoxes and Infinity
Mon, Tue, Wed, & Thurs, Jul 14 - Jul 16 (meets every day of the week!)

Intermediate: Grades 8-12

Intermediate Algebra
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
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3

Precalculus
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
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
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

AIME Problem Series A
Thursday, May 22 - Jul 31

AIME Problem Series B
Sunday, Jun 22 - Sep 21

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
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)
0 replies
jlacosta
May 1, 2025
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
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
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]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/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 $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ 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
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
100th post!!!
whwlqkd   12
N an hour ago by Leeoz
Hello,I am Seohyung Jo,8th grade student from South Korea. I couldn’t think I write many posts. But now,it is my 100th post!!!! As many people do these kind of posts(like 1000th post),I do this post.

Because this is my 100th post,I will share some problems:make 100

Make 100 with these numbers and +,-,*,/,!,^,nCr,nPr
Level 1(easy):20,25,30,35,40
Level 2(medium):1,3,4,5,7
Level 3(hard):1,2,3,4,5
Level 4(extreme):2,3,6,8,9
Level X:2,3,3,4,4
12 replies
whwlqkd
May 11, 2025
Leeoz
an hour ago
best times to work?
Spacepandamath13   11
N an hour ago by Craftybutterfly
What do you think are the best times to work on math or whatever?
11 replies
Spacepandamath13
Yesterday at 12:55 AM
Craftybutterfly
an hour ago
9 AMC 8 Scores
ChromeRaptor777   137
N an hour ago by valisaxieamc
As far as I'm certain, I think all AMC8 scores are already out. Vote above.
137 replies
ChromeRaptor777
Apr 1, 2022
valisaxieamc
an hour ago
9 What competitions do you do
VivaanKam   33
N an hour ago by valisaxieamc

I know I missed a lot of other competitions so if you didi one of the just choose "Other".
33 replies
VivaanKam
Apr 30, 2025
valisaxieamc
an hour ago
euler function
mathsearcher   0
2 hours ago
Prove that there exists infinitely many positive integers n such that
ϕ(n) | n+1
0 replies
mathsearcher
2 hours ago
0 replies
Simple but hard
Lukariman   1
N 3 hours ago by Giant_PT
Given triangle ABC. Outside the triangle, construct rectangles ACDE and BCFG with equal areas. Let M be the midpoint of DF. Prove that CM passes through the center of the circle circumscribing triangle ABC.
1 reply
Lukariman
4 hours ago
Giant_PT
3 hours ago
Floor function and coprime
mofumofu   13
N 3 hours ago by Thapakazi
Source: 2018 China TST 2 Day 2 Q4
Let $k, M$ be positive integers such that $k-1$ is not squarefree. Prove that there exist a positive real $\alpha$, such that $\lfloor \alpha\cdot k^n \rfloor$ and $M$ are coprime for any positive integer $n$.
13 replies
mofumofu
Jan 9, 2018
Thapakazi
3 hours ago
Old problem
kwin   0
3 hours ago
Let $ a, b, c > 0$ . Prove that:
$$(a^2+b^2)(b^2+c^2)(c^2+a^2)(ab+bc+ca)^2 \ge 8(abc)^2(a^2+b^2+c^2)^2$$
0 replies
kwin
3 hours ago
0 replies
Interesting inequalities
sqing   2
N 3 hours ago by sqing
Source: Own
Let $a,b,c \geq 0 $ and $ abc+2(ab+bc+ca) =32.$ Show that
$$ka+b+c\geq 8\sqrt k-2k$$Where $0<k\leq 4. $
$$ka+b+c\geq 8 $$Where $ k\geq 4. $
$$a+b+c\geq 6$$$$2a+b+c\geq 8\sqrt 2-4$$
2 replies
sqing
Yesterday at 2:51 PM
sqing
3 hours ago
RMM 2013 Problem 3
dr_Civot   79
N 3 hours ago by Ilikeminecraft
Let $ABCD$ be a quadrilateral inscribed in a circle $\omega$. The lines $AB$ and $CD$ meet at $P$, the lines $AD$ and $BC$ meet at $Q$, and the diagonals $AC$ and $BD$ meet at $R$. Let $M$ be the midpoint of the segment $PQ$, and let $K$ be the common point of the segment $MR$ and the circle $\omega$. Prove that the circumcircle of the triangle $KPQ$ and $\omega$ are tangent to one another.
79 replies
dr_Civot
Mar 2, 2013
Ilikeminecraft
3 hours ago
Inspired by KhuongTrang
sqing   7
N 3 hours ago by TNKT
Source: Own
Let $a,b,c\ge 0 $ and $ a+b+c=3.$ Prove that
$$\frac{1}{ab+2}+\frac{1}{bc+2}+\frac{1}{ca+2}\ge \frac{6}{abc+5}$$$$\frac{1}{ab+2}+\frac{1}{bc+2}+\frac{1}{ca+2}\ge \frac{7}{abc+6}$$$$\frac{1}{ab+2}+\frac{1}{bc+2}+\frac{1}{ca+2}\ge \frac{21}{17(abc+1)}$$$$\frac{1}{ab+2}+\frac{1}{bc+2}+\frac{1}{ca+2}\ge \frac{42}{17(abc+2)}$$
7 replies
sqing
Jan 21, 2024
TNKT
3 hours ago
Cycle in a graph with a minimal number of chords
GeorgeRP   5
N 3 hours ago by Photaesthesia
Source: Bulgaria IMO TST 2025 P3
In King Arthur's court every knight is friends with at least $d>2$ other knights where friendship is mutual. Prove that King Arthur can place some of his knights around a round table in such a way that every knight is friends with the $2$ people adjacent to him and between them there are at least $\frac{d^2}{10}$ friendships of knights that are not adjacent to each other.
5 replies
GeorgeRP
Wednesday at 7:51 AM
Photaesthesia
3 hours ago
Sum of bad integers to the power of 2019
mofumofu   8
N 4 hours ago by Orthocenter.THOMAS
Source: China TST 2019 Test 2 Day 2 Q6
Given coprime positive integers $p,q>1$, call all positive integers that cannot be written as $px+qy$(where $x,y$ are non-negative integers) bad, and define $S(p,q)$ to be the sum of all bad numbers raised to the power of $2019$. Prove that there exists a positive integer $n$, such that for any $p,q$ as described, $(p-1)(q-1)$ divides $nS(p,q)$.
8 replies
mofumofu
Mar 11, 2019
Orthocenter.THOMAS
4 hours ago
Collinearity with orthocenter
liberator   181
N 4 hours ago by Giant_PT
Source: IMO 2013 Problem 4
Let $ABC$ be an acute triangle with orthocenter $H$, and let $W$ be a point on the side $BC$, lying strictly between $B$ and $C$. The points $M$ and $N$ are the feet of the altitudes from $B$ and $C$, respectively. Denote by $\omega_1$ is the circumcircle of $BWN$, and let $X$ be the point on $\omega_1$ such that $WX$ is a diameter of $\omega_1$. Analogously, denote by $\omega_2$ the circumcircle of triangle $CWM$, and let $Y$ be the point such that $WY$ is a diameter of $\omega_2$. Prove that $X,Y$ and $H$ are collinear.

Proposed by Warut Suksompong and Potcharapol Suteparuk, Thailand
181 replies
liberator
Jan 4, 2016
Giant_PT
4 hours ago
1234th Post!
PikaPika999   262
N May 4, 2025 by PikaPika999
I hit my 1234th post! (I think I missed it, I'm kinda late, :oops_sign:)

But here's a puzzle for you all! Try to create the numbers 1 through 25 using the numbers 1, 2, 3, and 4! You are only allowed to use addition, subtraction, multiplication, division, and parenthesis. If you're post #1, try to make 1. If you're post #2, try to make 2. If you're post #3, try to make 3, and so on. If you're a post after 25, then I guess you can try to make numbers greater than 25 but you can use factorials, square roots, and that stuff. Have fun!

1: $(4-3)\cdot(2-1)$
262 replies
PikaPika999
Apr 21, 2025
PikaPika999
May 4, 2025
1234th Post!
G H J
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
PikaPika999
1899 posts
#1 • 14 Y
Y by Exponent11, MathDolphin95, jkim0656, EthanNg6, H1u2g4o4, tofubear, Yiyj1, RainbowJessa, aidan0626, MathNinja9, PikaIsChu12, CheckeredPenguin10, corgi61, wimpykid
I hit my 1234th post! (I think I missed it, I'm kinda late, :oops_sign:)

But here's a puzzle for you all! Try to create the numbers 1 through 25 using the numbers 1, 2, 3, and 4! You are only allowed to use addition, subtraction, multiplication, division, and parenthesis. If you're post #1, try to make 1. If you're post #2, try to make 2. If you're post #3, try to make 3, and so on. If you're a post after 25, then I guess you can try to make numbers greater than 25 but you can use factorials, square roots, and that stuff. Have fun!

1: $(4-3)\cdot(2-1)$
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
electric_pi
16 posts
#2 • 3 Y
Y by PikaPika999, RainbowJessa, PikaIsChu12
2: 4+2-1-3
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
iwastedmyusername
152 posts
#3 • 3 Y
Y by PikaPika999, RainbowJessa, PikaIsChu12
3=1+2*3-4
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Shan3t
373 posts
#4 • 2 Y
Y by PikaPika999, PikaIsChu12
$4:4\cdot(3-2\cdot1)$
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
evt917
2420 posts
#5 • 1 Y
Y by PikaPika999
5: 4 + (3-2*1)
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Shan3t
373 posts
#6 • 1 Y
Y by PikaPika999
$5:4+(3-2)\cdot1$
$6:3\cdot\frac42\cdot1$
$7:4+3(2-1).$

Thats all ill do
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Inaaya
378 posts
#7 • 1 Y
Y by PikaPika999
5: 4x2x1-3
ahh crap sniped
This post has been edited 1 time. Last edited by Inaaya, Apr 21, 2025, 9:08 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
RocketScientist
358 posts
#9 • 1 Y
Y by Ravensrule8
8: $3+4 - (1-2)$
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Inaaya
378 posts
#10 • 1 Y
Y by PikaPika999
8: (4-2)x(3+1)
WHAT THE SNIPE
This post has been edited 1 time. Last edited by Inaaya, Apr 21, 2025, 9:11 PM
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Inaaya
378 posts
#11 • 1 Y
Y by PikaPika999
9: 4x3-(2+1)
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Inaaya
378 posts
#12 • 1 Y
Y by PikaPika999
10: 4x2+3-1
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Inaaya
378 posts
#13 • 1 Y
Y by PikaPika999
11: 4x2 + (3/1)
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
RocketScientist
358 posts
#14 • 1 Y
Y by PikaPika999
12: $4*3*(2-1)$
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Shan3t
373 posts
#15 • 1 Y
Y by PikaPika999
$12= 4*3*(2-1)$
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Shan3t
373 posts
#16 • 1 Y
Y by PikaPika999
$13:4*3+(2-1)$
Z K Y
G
H
=
a