Art of Problem Solving
AoPS Online AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy AoPS Academy
Small live classes for advanced math
and language arts learners in grades 1-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Stay ahead of learning milestones! Enroll in a class over the summer!
No tags match your search
M
G
Topic
First Poster
Last Poster
H
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
J
H
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
J
H
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
J
H
Prove that the triangle is isosceles.
TUAN2k8   4
N 30 minutes ago by JARP091
Source: My book
Given acute triangle $ABC$ with two altitudes $CF$ and $BE$.Let $D$ be the point on the line $CF$ such that $DB \perp BC$.The lines $AD$ and $EF$ intersect at point $X$, and $Y$ is the point on segment $BX$ such that $CY \perp BY$.Suppose that $CF$ bisects $BE$.Prove that triangle $ACY$ is isosceles.
4 replies
TUAN2k8
Yesterday at 9:55 AM
JARP091
30 minutes ago
J
H
Pythagoras...
Hip1zzzil   0
30 minutes ago
Source: KMO 2025 Round 1 P20
Find the sum of all $k$s such that:
There exists two odd positive integers $a,b$ such that ${k}^{2}={a}^{2b}+{(2b)}^{4}.$
0 replies
Hip1zzzil
30 minutes ago
0 replies
J
H
Hard Function
johnlp1234   2
N 39 minutes ago by maromex
Find all function $f:\mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ such that:
$$f(x^3+f(y))=y+(f(x))^3$$
2 replies
johnlp1234
Jul 8, 2020
maromex
39 minutes ago
J
H
Guangxi High School Mathematics Competition 2025 Q12
sqing   3
N 44 minutes ago by sqing
Source: China Guangxi High School Mathematics Competition 2025 Q12
Let $ a,b,c>0 $. Prove that
$$abc\geq \frac {a+b+c}{\frac {1}{a^2}+\frac {1}{b^2}+\frac {1}{c^2} }\geq(a+b-c)(b+c-a)(c+a-b)$$
3 replies
sqing
an hour ago
sqing
44 minutes ago
J
H
msm level cdr questions
Soupboy0   25
N an hour ago by nmlikesmath
ima post cdr level questions and the first person to answer (may) admit orz

1st question:

If $6$ sigmas = $41$ looksmaxxers, and $2$ looksmaxxers = $13$ skibdis, how many skibidis are in a sigma? Express your answer as a common fraction


orziest people
25 replies
Soupboy0
Yesterday at 2:35 AM
nmlikesmath
an hour ago
J
H
9 Am I going insane?
PenguFish   25
N an hour ago by nmlikesmath
I feel stupid honestly, and fyi, I did go over every question. Focus is counting with symmetry
25 replies
PenguFish
Mar 26, 2025
nmlikesmath
an hour ago
J
H
Hard Function
johnlp1234   4
N an hour ago by jasperE3
f:R+--->R+:
f(x^3+f(y))=y+(f(x))^3
4 replies
johnlp1234
Jul 7, 2020
jasperE3
an hour ago
J
H
9 What competitions do you do
VivaanKam   37
N an hour ago by whwlqkd

I know I missed a lot of other competitions so if you didi one of the just choose "Other".
37 replies
VivaanKam
Apr 30, 2025
whwlqkd
an hour ago
J
H
Pythagorean Diophantine?
youochange   2
N an hour ago by Ianis
The number of ordered pair $(a,b)$ of positive integers with $a \le b$ satisfying $a^2+b^2=2025$ is

Click to reveal hidden text
2 replies
youochange
2 hours ago
Ianis
an hour ago
J
H
A china olympia 2015 problem.
Math2030   0
2 hours ago
Let $n \geq 5$ be a positive integer and let $A$ and $B$ be sets of integers satisfying the following conditions:

i) $|A| = n$, $|B| = m$ and $A$ is a subset of $B$
ii) For any distinct $x,y \in B$, $x+y \in B$ iff $x,y \in A$

Determine the minimum value of $m$.
0 replies
Math2030
2 hours ago
0 replies
J
H
9 1000th POST!!!!!!!
thegreatbrain   60
N 2 hours ago by FredyCrooger
THIS IS MY 1000TH POST!!!!!!!!!!!
60 replies
thegreatbrain
Thursday at 7:44 PM
FredyCrooger
2 hours ago
J
H
Permutations of Integers from 1 to n
Twoisntawholenumber   75
N 4 hours ago by SYBARUPEMULA
Source: 2020 ISL C1
Let $n$ be a positive integer. Find the number of permutations $a_1$, $a_2$, $\dots a_n$ of the
sequence $1$, $2$, $\dots$ , $n$ satisfying
$$a_1 \le 2a_2\le 3a_3 \le \dots \le na_n$$.

Proposed by United Kingdom
75 replies
Twoisntawholenumber
Jul 20, 2021
SYBARUPEMULA
4 hours ago
J
H
Again
heartwork   11
N 4 hours ago by Mathandski
Source: Vietnam MO 2002, Problem 5
Determine for which $ n$ positive integer the equation: $ a + b + c + d = n \sqrt {abcd}$ has positive integer solutions.
11 replies
heartwork
Dec 16, 2004
Mathandski
4 hours ago
J
H
Cono Sur Olympiad 2011, Problem 3
Leicich   5
N 4 hours ago by Thelink_20
Let $ABC$ be an equilateral triangle. Let $P$ be a point inside of it such that the square root of the distance of $P$ to one of the sides is equal to the sum of the square roots of the distances of $P$ to the other two sides. Find the geometric place of $P$.
5 replies
Leicich
Aug 23, 2014
Thelink_20
4 hours ago
J
H
J
H
k 100 post!
JohannIsBach   13
N Apr 18, 2025 by EthanNg6
this is my 100th post! i cant believe it. :wow:
P.S. can everyone who reads this give it an upvote? thx!
13 replies
JohannIsBach
Mar 10, 2025
EthanNg6
Apr 18, 2025
J
100 post!
G H J
Reveal topic tags
Celebration
L
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.
JohannIsBach
207 posts
JohannIsBach
#1 h  Mar 10, 2025, 4:07 PM • 43 Y
Y by sangriabeaver5, valenbb, mithu542, apex304, Pi_isCool31415, GlitchyBoy, MathRook7817, Aaronjudgeisgoat, imagien_bad, Soupboy0, HenryJW, BigOrca, alexanderhamilton124, WoodBurnerB, Squidget, Exponent11, Shaarav14, stjwyl, PenguFish, evt917, vmene, mathkidAP, littlebigbull, valisaxieamc, Demetri, Yolandayu, DhruvJha, tliang2000, ChocolateEruption, Dolphincurious79, MathDolphin95, Pengu14, ktokita, Robert00, EthanNg6, FunnyKoala17, Ruegerbyrd, pasketti31415, Bocabulary142857, PikaPika999, ScrappyBoss0825, MathLoverYeah, NovaFrost
this is my 100th post! i cant believe it. :wow:
P.S. can everyone who reads this give it an upvote? thx!
This post has been edited 1 time. Last edited by JohannIsBach, Mar 10, 2025, 4:08 PM
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
MathRook7817
744 posts
MathRook7817
#2 h  Mar 10, 2025, 6:44 PM • 2 Y
Y by EthanNg6, PikaPika999
congrats
now u need 900 more to 1000!
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
imagien_bad
58 posts
imagien_bad
#3 h  Mar 10, 2025, 6:55 PM • 1 Y
Y by PikaPika999
MathRook7817 wrote:
congrats
now u need 900 more to 1000!

:cleaning: :furious: :diablo:
1000! - 900 >>>>>>>> 100
rbo
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Soupboy0
449 posts
Soupboy0
#4 h  Mar 10, 2025, 6:58 PM • 1 Y
Y by Cinnamon.-.Roll
actually you would need $4.0238726 \cdot 10^{2567}$ more posts to get to 1000!
This post has been edited 1 time. Last edited by Soupboy0, Mar 10, 2025, 6:58 PM
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
ChocolateEruption
16 posts
ChocolateEruption
#5 h  Mar 10, 2025, 6:58 PM
Y by
JohannIsBach wrote:
this is my 100th post! i cant believe it. :wow:
P.S. can everyone who reads this give it an upvote? thx!

nice your 1/10 of the way :jump:
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
wuwang2002
1215 posts
wuwang2002
#6 h  Mar 10, 2025, 9:58 PM • 1 Y
Y by Cinnamon.-.Roll
MathRook7817 wrote:
congrats
now u need 900 more to 1000!

r/unexpectedfactorial
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
PenguFish
25 posts
PenguFish
#7 h  Mar 10, 2025, 10:01 PM
Y by
Wow, I only have 7 -_-
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
skillfulapple
34 posts
skillfulapple
#8 h  Mar 10, 2025, 10:02 PM
Y by
u just need $7!-4940$ more 2 go
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
valisaxieamc
470 posts
valisaxieamc
#9 h  Mar 10, 2025, 11:38 PM
Y by
I need like 74 more to 100 so..
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Soupboy0
449 posts
Soupboy0
#10 h  Mar 10, 2025, 11:45 PM
Y by
you actually need 73
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Yolandayu
580 posts
Yolandayu
#11 h  Mar 10, 2025, 11:57 PM
Y by
What should my next goal be?
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
valisaxieamc
470 posts
valisaxieamc
#12 h  Mar 11, 2025, 1:46 AM
Y by
Yolandayu wrote:
What should my next goal be?

like 750 then 1000
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Dolphincurious79
551 posts
Dolphincurious79
#14 h  Apr 18, 2025, 7:11 PM
Y by
I don't post much on AoPS made forums
I post a lot more on user made forums though
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
EthanNg6
35 posts
EthanNg6
#15 h  Apr 18, 2025, 11:56 PM • 1 Y
Y by Exponent11
Congrats
Z Y
G
H
=
a