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k a My Retirement & New Leadership at AoPS
rrusczyk   1571
N Mar 26, 2025 by SmartGroot
I write today to announce my retirement as CEO from Art of Problem Solving. When I founded AoPS 22 years ago, I never imagined that we would reach so many students and families, or that we would find so many channels through which we discover, inspire, and train the great problem solvers of the next generation. I am very proud of all we have accomplished and I’m thankful for the many supporters who provided inspiration and encouragement along the way. I'm particularly grateful to all of the wonderful members of the AoPS Community!

I’m delighted to introduce our new leaders - Ben Kornell and Andrew Sutherland. Ben has extensive experience in education and edtech prior to joining AoPS as my successor as CEO, including starting like I did as a classroom teacher. He has a deep understanding of the value of our work because he’s an AoPS parent! Meanwhile, Andrew and I have common roots as founders of education companies; he launched Quizlet at age 15! His journey from founder to MIT to technology and product leader as our Chief Product Officer traces a pathway many of our students will follow in the years to come.

Thank you again for your support for Art of Problem Solving and we look forward to working with millions more wonderful problem solvers in the years to come.

And special thanks to all of the amazing AoPS team members who have helped build AoPS. We’ve come a long way from here:IMAGE
1571 replies
rrusczyk
Mar 24, 2025
SmartGroot
Mar 26, 2025
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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 2025
0 replies
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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
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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
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x+y+z=0 inequality
KhuongTrang   1
N a few seconds ago by Nguyenhuyen_AG
Source: own
Problem. Let $x,y,z\in\mathbb{R}: x+y+z=0$ then prove $$\color{blue}{\frac{x+1}{x^2+8}+\frac{y+1}{y^2+8}+\frac{z+1}{z^2+8}\le \frac{3}{8}.}$$Equality holds iff $(x,y,z)\sim(0,0,0)$ or $(x,y,z)\sim(2,2,-4).$
1 reply
KhuongTrang
38 minutes ago
Nguyenhuyen_AG
a few seconds ago
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Infinite sequences.. welp
navi_09220114   5
N 3 minutes ago by AN1729
Source: Own. Malaysian IMO TST 2025 P1
Determine all integers $n\ge 2$ such that for any two infinite sequences of positive integers $a_1<a_2< \cdots $ and $b_1, b_2, \cdots$, such that $a_i\mid a_j$ for all $i<j$, there always exists a real number $c$ such that $$\lfloor{ca_i}\rfloor \equiv b_i \pmod {n}$$for all $i\ge 1$.

Proposed by Wong Jer Ren & Ivan Chan Kai Chin
5 replies
navi_09220114
Mar 22, 2025
AN1729
3 minutes ago
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Calculating combinatorial numbers
lgx57   0
9 minutes ago
Try to simplify this expression:

$$\sum_{i=1}^n \sum_{j=1}^i C_{n}^i C_{n}^j$$
0 replies
lgx57
9 minutes ago
0 replies
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Hard number theory
Hip1zzzil   5
N 10 minutes ago by Lufin
Source: FKMO 2025 P6
Two positive integers $a,b$ satisfy the following two conditions:

1) $m^{2}|ab \Rightarrow m=1$
2) Integers $x,y,z,w$ exist such that $ax^{2}+by^{2}=z^{2}+w^{2}, w^{2}+z^{2}>0$.

Prove that for any positive integer $n$,
Positive integers $x,y,z,w$ exist such that $ax^{2}+by^{2}+n=z^{2}+w^{2}$.
5 replies
Hip1zzzil
2 hours ago
Lufin
10 minutes ago
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Maximum number of Sets
pokmui9909   3
N 12 minutes ago by Acorn-SJ
Source: FKMO 2025 P5
For a subset $T$ of the set $S = \{1, 2, \dots, 1000\}$, let $\tilde{T} = \{1001 - t \ | \ t \in T\}$. Find the maximum number of elements in the set $\mathcal{P}$ that satisfies all of the three following conditions:
[list]
[*] All elements of $\mathcal{P}$ are subsets of $S$.
[*] For any two elements $A, B$ of $\mathcal{P}$, $A\cap B$ is not empty.
[*] For any element $A$ of $\mathcal{P}$, $\tilde{A} \in \mathcal{P}$.
[/list]
3 replies
pokmui9909
2 hours ago
Acorn-SJ
12 minutes ago
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Equality case being all distinct reals?
navi_09220114   2
N 12 minutes ago by AN1729
Source: Own. Malaysian IMO TST 2025 P7
Given a real polynomial $P(x)=a_{2024}x^{2024}+\cdots+a_1x+a_0$ with degree $2024$, such that for all positive reals $b_1, b_2,\cdots, b_{2025}$ with product $1$, then; $$P(b_1)+P(b_2)+\cdots +P(b_{2025})\ge 0$$Suppose there exist positive reals $c_1, c_2, \cdots, c_{2025}$ with product $1$, such that; $$P(c_1)+P(c_2)+ \cdots +P(c_{2025})=0$$Is it possible that the values $c_1, c_2, \cdots, c_{2025}$ are all distinct?

Proposed by Ivan Chan Kai Chin
2 replies
navi_09220114
Mar 22, 2025
AN1729
12 minutes ago
J
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closure subsets
lgx57   0
12 minutes ago
Let $S_1,S_2 \cdots S_n$ are proper subsets of $\mathbb{R}$ and they are closed for addition and subtraction. Try to prove that:

$$\displaystyle\bigcup_{i=1}^n S_i \ne \mathbb{R}$$
0 replies
lgx57
12 minutes ago
0 replies
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FE f(x)f(y)+1=f(x+y)+f(xy)+xy(x+y-2)
steven_zhang123   1
N 13 minutes ago by pco
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x,y \in \mathbb{R}$, we have $f(x)f(y)+1=f(x+y)+f(xy)+xy(x+y-2)$.
1 reply
steven_zhang123
Yesterday at 11:27 PM
pco
13 minutes ago
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Inspired by KHOMNYO2
sqing   1
N 15 minutes ago by truongphatt2668
Source: Own
Let $ a,b,c>0 $ and $ a^2+b^2+c^2=3. $ Prove that $$ \frac{2}{a} + \frac{2}{b} + \frac{2}{c} +a + b +c+ abc\geq 10$$
1 reply
sqing
Friday at 2:46 PM
truongphatt2668
15 minutes ago
J
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Graph vertices with degree
MetaphysicalWukong   0
20 minutes ago
Source: Qianrong Hao
For a graph $G=\left(V,E\right)$, what is the largest possible value of |V| if |E|=35 and $deg\left(v\right)\ge3$
0 replies
1 viewing
MetaphysicalWukong
20 minutes ago
0 replies
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Functional Equations Marathon March 2025
Levieee   25
N 26 minutes ago by Jupiterballs
1. before posting another problem please try your best to provide the solution to the previous solution because we don't want a backlog of many problems
2.one is welcome to send functional equations involving calculus (mainly basic real analysis type of proofs) as long it is of the form $\text{"find all functions:"}$
25 replies
Levieee
Mar 17, 2025
Jupiterballs
26 minutes ago
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A checkered square consists of dominos
nAalniaOMliO   2
N 42 minutes ago by weamher
Source: Belarusian National Olympiad 2025
A checkered square $8 \times 8$ is divided into rectangles with two cells. Two rectangles are called adjacent if they share a segment of length 1 or 2. In each rectangle the amount of adjacent with it rectangles is written.
Find the maximal possible value of the sum of all numbers in rectangles.
2 replies
nAalniaOMliO
Friday at 8:21 PM
weamher
42 minutes ago
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Great orz
Hip1zzzil   3
N an hour ago by Acorn-SJ
Source: FKMO 2025 P5
$S={1,2,...,1000}$ and $T'=\left\{ 1001-t|t \in T\right\}$.
A set $P$ satisfies the following three conditions:
$1.$ All elements of $P$ are a subset of $S$.
$2. A,B \in P \Rightarrow A \cap B \neq \O$
$3. A \in P \Rightarrow A' \in P$
Find the maximum of $|P|$.
3 replies
Hip1zzzil
2 hours ago
Acorn-SJ
an hour ago
J
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Age proof
Mathskidd   1
N an hour ago by ohiorizzler1434
$$ $$

As the diagram shown

By means of contrusting semi circle with diamieter as length of $a+b$, then

Its radius is $\frac {a+b}2 $. Half chord $GQ=\sqrt {ab}$

Obviously, ie. When $n=2, \frac {a+b}2 \geq \sqrt {ab}$
Equality holds when $a=b$
1 reply
Mathskidd
an hour ago
ohiorizzler1434
an hour ago
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i need help
MR.1   6
N Mar 27, 2025 by GreekIdiot
Source: help
can you guys tell me problems about fe in $R+$(i know $R$ well). i want to study so if you guys have some easy or normal problems please send me
6 replies
MR.1
Mar 15, 2025
GreekIdiot
Mar 27, 2025
J
i need help
G H J
Reveal topic tags
functional equation
L
G H BBookmark kLocked kLocked NReply
Source: help
The post below has been deleted. Click to close.
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MR.1
91 posts
MR.1
#1 h  Mar 15, 2025, 10:11 AM
Y by
can you guys tell me problems about fe in $R+$(i know $R$ well). i want to study so if you guys have some easy or normal problems please send me
Z K Y
The post below has been deleted. Click to close.
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MR.1
91 posts
MR.1
#2 h  Mar 15, 2025, 12:29 PM
Y by
help please :(
Z K Y
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whwlqkd
66 posts
whwlqkd
#4 h  Mar 15, 2025, 12:44 PM
Y by
R+ FE from somewhere in South Korea:
Find all function f:R+ ->R+ that for every positive real x,y , we get f(xy+f(xy))=xf(y)+yf(x)
Z K Y
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MR.1
91 posts
MR.1
#5 h  Mar 15, 2025, 12:50 PM
Y by
thank you
:-D
Z K Y
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GreekIdiot
139 posts
GreekIdiot
#6 h  Mar 26, 2025, 3:41 PM
Y by
Try this one
Find all $f: \mathbb R_+ \rightarrow \mathbb R_+$ such that $f(xf(y)+f(x))=yf(x+yf(x)) \: \forall \: x,y \in \mathbb R_+$
Z K Y
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hanzo.ei
11 posts
hanzo.ei
#8 h  Mar 27, 2025, 4:51 PM
Y by
GreekIdiot wrote:
Try this one
Find all $f: \mathbb R_+ \rightarrow \mathbb R_+$ such that $f(xf(y)+f(x))=yf(x+yf(x)) \: \forall \: x,y \in \mathbb R_+$
can you give me solution for this problem
Z K Y
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GreekIdiot
139 posts
GreekIdiot
#9 h  Mar 27, 2025, 5:09 PM
Y by
Havent solved myself, just heard this one is hard and very beautiful ...
On a first look I think $f$ is an involution, maybe proving injectivity and surjectivity, then this...
On a quick sketch of the solution I found $f(x)=0$ which doesnt work, $f(x)=x$ which doesnt work and $f(x)=\dfrac{1}{x}$ which works
Z K Y
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