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

Happy Memorial Day! Please note that AoPS Online is closed May 24-26th.
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 
18,673 topics
w
6 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
3D geometry
Greed Control
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 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
banned myself from own blog
Spacepandamath13   4
N 10 minutes ago by Demetri
I got curious and decided to see if I can ban myself from my own blog.
can site admins give it back? it says site admins are the administrators of this blog

I honestly don't know where I come up with stuff like this
4 replies
Spacepandamath13
Today at 3:02 AM
Demetri
10 minutes ago
J
H
How to create a poll?
whwlqkd   19
N 22 minutes ago by EP1
How to create a poll in aops?
19 replies
whwlqkd
Today at 12:24 PM
EP1
22 minutes ago
J
H
Cool Functional Equation
Warideeb   1
N 34 minutes ago by maromex
Find all functions real to real such that
$f(xy+f(x))=xf(y)+f(x)$
for all reals $x,y$.
1 reply
Warideeb
2 hours ago
maromex
34 minutes ago
J
H
Functional equation
socrates   10
N 41 minutes ago by MathLuis
Source: Inspired by another
Determine all functions $f : \mathbb{R}^+ \to \mathbb{R}^+$ such that \[ \forall x, y \in \mathbb{R}^+ \ , \ \ f(x+f(xy))=f(x)+xf(y).\]
10 replies
socrates
Oct 28, 2014
MathLuis
41 minutes ago
J
H
Find f
Redriver   7
N an hour ago by aaravdodhia
Find all $: R \to R : \ \ f(x^2+f(y))=y+f^2(x)$
7 replies
Redriver
Jun 25, 2006
aaravdodhia
an hour ago
J
H
IMO Shortlist 2011, G5
WakeUp   72
N an hour ago by ItsBesi
Source: IMO Shortlist 2011, G5
Let $ABC$ be a triangle with incentre $I$ and circumcircle $\omega$. Let $D$ and $E$ be the second intersection points of $\omega$ with $AI$ and $BI$, respectively. The chord $DE$ meets $AC$ at a point $F$, and $BC$ at a point $G$. Let $P$ be the intersection point of the line through $F$ parallel to $AD$ and the line through $G$ parallel to $BE$. Suppose that the tangents to $\omega$ at $A$ and $B$ meet at a point $K$. Prove that the three lines $AE,BD$ and $KP$ are either parallel or concurrent.

Proposed by Irena Majcen and Kris Stopar, Slovenia
72 replies
WakeUp
Jul 13, 2012
ItsBesi
an hour ago
J
H
Hard Functional Equation in the Complex Numbers
yaybanana   5
N an hour ago by aaravdodhia
Source: Own
Find all functions $f:\mathbb {C}\rightarrow \mathbb {C}$, s.t :

$f(xf(y)) + f(x^2+y) = f(x+y)x + f(f(y))$

for all $x,y \in \mathbb{C}$
5 replies
yaybanana
Apr 9, 2025
aaravdodhia
an hour ago
J
H
Power tower sum
Rijul saini   9
N an hour ago by ihategeo_1969
Source: India IMOTC 2024 Day 3 Problem 2
Let $a$ and $n$ be positive integers such that:
1. $a^{2^n}-a$ is divisible by $n$,
2. $\sum\limits_{k=1}^{n} k^{2024}a^{2^k}$ is not divisible by $n$.

Prove that $n$ has a prime factor smaller than $2024$.

Proposed by Shantanu Nene
9 replies
Rijul saini
May 31, 2024
ihategeo_1969
an hour ago
J
H
Nice "if and only if" function problem
ICE_CNME_4   7
N an hour ago by ICE_CNME_4
Let $f : [0, \infty) \to [0, \infty)$, $f(x) = \dfrac{ax + b}{cx + d}$, with $a, d \in (0, \infty)$, $b, c \in [0, \infty)$. Prove that there exists $n \in \mathbb{N}^*$ such that for every $x \geq 0$
\[ f_n(x) = \frac{x}{1 + nx}, \quad \text{if and only if } f(x) = \frac{x}{1 + x}, \quad \forall x \geq 0. \](For $n \in \mathbb{N}^*$ and $x \geq 0$, the notation $f_n(x)$ represents $\underbrace{(f \circ f \circ \dots \circ f)}_{n \text{ times}}(x)$. )

Please do it at 9th grade level. Thank you!
7 replies
ICE_CNME_4
Yesterday at 7:23 PM
ICE_CNME_4
an hour ago
J
H
Cauchy-Schwarz 2
prtoi   8
N an hour ago by mrtheory
Source: Handout by Samin Riasat
if $a^2+b^2+c^2+d^2=4$, prove that:
$\frac{a^2}{b}+\frac{b^2}{c}+\frac{c^2}{d}+\frac{d^2}{a}\ge4$
8 replies
prtoi
Mar 26, 2025
mrtheory
an hour ago
J
H
D1037 : The super irreductibilty
Dattier   1
N 2 hours ago by Dattier
Source: les dattes à Dattier
Let $P \in \mathbb Q[x]$, $P$ is super irreductible if $\forall Q \in \mathbb [x], \deg(Q)>0, P(Q(x))$ is irreductible.

Are there some $P \in \mathbb Q[x]$ super irreductible?
1 reply
Dattier
3 hours ago
Dattier
2 hours ago
J
H
FE on Stems
mathscrazy   7
N 2 hours ago by Thapakazi
Source: STEMS 2025 Category B4, C3
Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that for all $x,y\in \mathbb{R}$, \[xf(y+x)+(y+x)f(y)=f(x^2+y^2)+2f(xy)\]Proposed by Aritra Mondal
7 replies
mathscrazy
Dec 29, 2024
Thapakazi
2 hours ago
J
H
resolved!
JohannIsBach   6
N Today at 2:55 AM by bpan2021
hi srry if this is in the rong place i didnt no where 2 put it i was wondering how u find a user? i tried using the search but they dont have any posts? dont no wat 2 do...
6 replies
JohannIsBach
Today at 12:57 AM
bpan2021
Today at 2:55 AM
J
H
Stamina XP decreasing?
Craftybutterfly   15
N Yesterday at 3:01 PM by Craftybutterfly
Summary of the problem: Last night when I checked, alcumus said I had 4250 stamina XP which is more than other people. However, when I just checked, it said I only earned 3905 XP. What is wrong?
Page URL: Hall of Fame
Steps to reproduce:
1. Go to hall of fame
2. Scroll to stamina XP earned
Expected behavior: It should still say I earned 4250 XP
Frequency: 100%
Operating system(s): HP Elitebook
Browser(s), including version: Chrome
IMAGE
15 replies
Craftybutterfly
May 22, 2025
Craftybutterfly
Yesterday at 3:01 PM
J
H
J
H
k **RESOLVED** Boxed in LaTeX Question
PikaPika999   2
N Apr 9, 2025 by PikaPika999
In $\LaTeX$$,$ what is the difference between \boxed and \fbox?
2 replies
PikaPika999
Apr 9, 2025
PikaPika999
Apr 9, 2025
J
**RESOLVED** Boxed in LaTeX Question
G H J
Reveal topic tags
LaTeX
L
G H BBookmark kLocked kLocked NReply
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
PikaPika999
2286 posts
PikaPika999
#1 h  Apr 9, 2025, 1:07 AM
Y by
In $\LaTeX$$,$ what is the difference between \boxed and \fbox?
This post has been edited 1 time. Last edited by PikaPika999, Apr 9, 2025, 12:50 PM
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Demetri
1403 posts
Demetri
#2 h  Apr 9, 2025, 1:10 AM • 3 Y
Y by RollingPanda4616, jkim0656, PikaPika999
I would move this to the LaTeX and Asymptote forum.
This may give you the answer you seek.
This post has been edited 1 time. Last edited by Demetri, Apr 9, 2025, 1:11 AM
Z Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
PikaPika999
2286 posts
PikaPika999
#4 h  Apr 9, 2025, 12:50 PM
Y by
Ok thank you! :)
Z Y
G
H
=
a