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

Join our FREE webinar on May 1st to learn about managing anxiety.
Site Support Tech support and questions about AoPS classes and materials
Tech support and questions about AoPS classes and materials
3 M G
BBookmark  VNew Topic kLocked
Site Support Tech support and questions about AoPS classes and materials
Tech support and questions about AoPS classes and materials
3 M G
BBookmark  VNew Topic kLocked
t 
18,637 topics
w
2 users
TOPICS
No tags match your search
M
Alcumus
blogs
LaTeX
search
FTW
geometry
Support
email
MATHCOUNTS
function
AMC
AoPSwiki
Bug
Reaper
Forums
AIME
suggestion
poll
site support
AMC 10
AoPS
Asymptote
AoPS classes
videos
posts
Glitch
pms
calculus
Suggestions
help
probability
classroom
number theory
classes
AMC 8
AoPS Books
question
Forum
glitch or bug
Greed Control
3D geometry
AIME I
USA(J)MO
Tags
Friends
Homework
Avatars
BBCode
upvotes
Post
No tags match your search
M
G
Topic
First Poster
Last Poster
H
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
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
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
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
Monday, Jun 16 - Dec 8
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
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
jlacosta
Apr 2, 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
Inequality with condition a+b+c = ab+bc+ca (and special equality case)
DoThinh2001   69
N 21 minutes ago by mihaig
Source: BMO 2019, problem 2
Let $a,b,c$ be real numbers such that $0 \leq a \leq b \leq c$ and $a+b+c=ab+bc+ca >0.$
Prove that $\sqrt{bc}(a+1) \geq 2$ and determine the equality cases.

(Edit: Proposed by sir Leonard Giugiuc, Romania)
69 replies
DoThinh2001
May 2, 2019
mihaig
21 minutes ago
J
H
1 line solution to Inequality
ItzsleepyXD   1
N 23 minutes ago by mihaig
Source: Own , Mock Thailand Mathematic Olympiad P8
Let $x_1,x_2,\dots,x_n$ be positive real integer such that $x_1^2+x_2^2+\cdots+x_n^2=2$ Prove that
$$\sum_{i=1}^{n}\frac{1}{x_i^3(x_{i-1}+x_{i+1})}\geqslant \left(\sum_{i=1}^{n}\frac{x_i}{x_{i-1}+x_{i+1}}\right)^3$$such that $x_{n+1}=x_1$ and $x_0=x_n$
1 reply
ItzsleepyXD
5 hours ago
mihaig
23 minutes ago
J
H
a nice problem of nt from PUMaC
Namisgood   1
N 25 minutes ago by Goutamioqmtopper
Source: PUMaC
Problem is attached
1 reply
Namisgood
Yesterday at 9:47 AM
Goutamioqmtopper
25 minutes ago
J
H
Diophantine equation !
ComplexPhi   11
N 26 minutes ago by Goutamioqmtopper
Determine all triples $(m , n , p)$ satisfying :
\[n^{2p}=m^2+n^2+p+1\]
where $m$ and $n$ are integers and $p$ is a prime number.
11 replies
ComplexPhi
Feb 4, 2015
Goutamioqmtopper
26 minutes ago
J
H
Solve $\sin(17x)+\sin(13x)=\sin(7x)$
Speed2001   1
N 32 minutes ago by rchokler
How to solve the equation:
$$ \sin(17x)+\sin(13x)=\sin(7x),\;0<x<24^{\circ} $$Approach: I'm trying to factor $\sin(18x)$ to get $x=10^{\circ}$.

Any hint would be appreciated.
1 reply
1 viewing
Speed2001
Yesterday at 1:06 AM
rchokler
32 minutes ago
J
H
7^a - 3^b divides a^4 + b^2 (from IMO Shortlist 2007)
Dida Drogbier   39
N 33 minutes ago by ND_
Source: ISL 2007, N1, VAIMO 2008, P4
Find all pairs of natural numbers $ (a, b)$ such that $ 7^a - 3^b$ divides $ a^4 + b^2$.

Author: Stephan Wagner, Austria
39 replies
Dida Drogbier
Apr 21, 2008
ND_
33 minutes ago
J
H
Inspired by tom-nowy
sqing   0
33 minutes ago
Source: Own
Let $a,b,c \in [-\frac{1}{2}, \frac{1}{2}]$. Prove that
$$ \frac{1}{16}\geq (ab+bc+ca)^2+ a^2b^2c^2-(a+b+c)^2\geq -\frac{107}{64} $$$$ \frac{1}{16}\geq (ab+bc+ca)^2+3a^2b^2c^2-(a+b+c)^2\geq -\frac{105}{64} $$Let $a,b,c \in [-2,2]$. Prove that
$$172\geq (ab+bc+ca)^2+ a^2b^2c^2-(a+b+c)^2\geq -\frac{64}{11} $$$$300\geq (ab+bc+ca)^2+3a^2b^2c^2-(a+b+c)^2\geq -\frac{192}{35} $$
0 replies
sqing
33 minutes ago
0 replies
J
H
An amazing inequality
Kei0923   6
N 34 minutes ago by Kei0923
Source: Own (2021 Mock Japan MO Finals 5)
Let $n$ be a positive integer and $a_{1},a_{2},\dots, a_{n+1}$ be positive real numbers such that $$\displaystyle {\sum_{i=1}^{n+1}}\frac{1}{a_{i}+n^2}=\frac{1}{n}.$$Prove that $$\sum_{i=1}^{n+1} \frac{1}{a_{i}^{2021}+n^{2020}} \geq \frac{1}{n^{2020}}.$$
6 replies
Kei0923
Mar 14, 2021
Kei0923
34 minutes ago
J
H
Prime Numbers
TRcrescent27   7
N 36 minutes ago by Goutamioqmtopper
Source: 2015 Turkey JBMO TST
Let $p,q$ be prime numbers such that their sum isn't divisible by $3$. Find the all $(p,q,r,n)$ positive integer quadruples satisfy:
$$p+q=r(p-q)^n$$
Proposed by Şahin Emrah
7 replies
TRcrescent27
Jun 22, 2016
Goutamioqmtopper
36 minutes ago
J
H
Ugly Inequality
EthanWYX2009   1
N an hour ago by NTstrucker
Show that
\[\sum_{k=1}^n\frac{\phi(k)}k\ln\frac{2^k}{2^k-1}\ge 1-\frac 1{2^n}.\]
1 reply
+1 w
EthanWYX2009
2 hours ago
NTstrucker
an hour ago
J
H
Introducing myself at AoPS, and what's your magic wand?
asuth_asuth   1049
N 2 hours ago by awesometriangles
Hi!

I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.

Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops

I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.
1049 replies
asuth_asuth
Mar 30, 2025
awesometriangles
2 hours ago
J
H
This has been going on for a while now, can anyone else relate?
jmr2010   2
N Today at 3:02 AM by valisaxieamc
Most of the time when I type in something for the tags or search for a user, the AoPS suggestion box pops up, and most of the time, when I click the suggestion, the box just disappears, meaning the automatic system usually never works
2 replies
jmr2010
Yesterday at 7:16 PM
valisaxieamc
Today at 3:02 AM
J
H
Cannot post PHP
char0221   2
N Today at 2:01 AM by bpan2021
Summary of the problem: If I try to post anything with PHP (a coding language), it
Page URL: In any forum or private messages
Steps to reproduce:
1. Create a post.
2. Put some PHP inside, can't give example
Expected behavior: Should post the message
Frequency: 100%
Operating system(s): macOS Sequoia 15.2.1
Browser(s), including version: Safari
Additional information: See attachments
2 replies
char0221
Today at 1:23 AM
bpan2021
Today at 2:01 AM
J
H
k How to remove tags from a PM after you've removed yourself from it
Platinum_Dragon   2
N Yesterday at 7:32 PM by Platinum_Dragon
Is it possible? Because it's kind of annoying to have a whole bunch of tags that stick around forever.

thank you
2 replies
Platinum_Dragon
Yesterday at 7:25 PM
Platinum_Dragon
Yesterday at 7:32 PM
J
H
J
H
k Upvote Glitch
henry24816   1
N Sep 5, 2016 by levans
When I was viewing this post, it had 107 upvotes.

IMAGE

Then I refreshed and it only had 1.
1 reply
henry24816
Sep 5, 2016
levans
Sep 5, 2016
J
Upvote Glitch
G H J
Reveal topic tags
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.
henry24816
268 posts
henry24816
#1 h  Sep 5, 2016, 10:20 PM • 4 Y
Y by Generic_Username, Samchooo, Adventure10, Mango247
When I was viewing this post, it had 107 upvotes.

http://image.prntscr.com/image/ab1a5500e9254e42be43265f9fb6c6ec.png

Then I refreshed and it only had 1.
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
levans
5190 posts
levans
#2 h  Sep 5, 2016, 10:22 PM • 5 Y
Y by henry24816, Generic_Username, Samchooo, Adventure10, Mango247
Strange issue. Thanks for pointing this out.
Z Y
G
H
=
a