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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]
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.

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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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Fibonacci sequence and primes
vicentev   0
10 minutes ago
Source: TST IMO CHILE 2025
Let \( u_n \) be the \( n \)-th term of the Fibonacci sequence (where \( u_1 = u_2 = 1 \) and \( u_{n+1} = u_n + u_{n-1} \) for \( n \geq 2 \)). For each prime \( p \), let \( n(p) \) be the smallest integer \( n \) such that \( u_n \) is divisible by \( p \). Find the smallest possible value of \( p - n(p) \).
0 replies
vicentev
10 minutes ago
0 replies
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Gheorghe Țițeica 2025 Grade 7 P3
AndreiVila   1
N 11 minutes ago by Rainbow1971
Source: Gheorghe Țițeica 2025
Out of all the nondegenerate triangles with positive integer sides and perimeter $100$, find the one with the smallest area.
1 reply
AndreiVila
Yesterday at 8:41 PM
Rainbow1971
11 minutes ago
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functional equations
sefatod628   6
N 11 minutes ago by pco
Source: Oral ENS
Hello guys, here is a fun functional equation !
Find all functions from $\mathbb{R^*_+}$ to $\mathbb{R^*_+}$ such that for all $x$ : $$f(f(x))=-f(x)+6x$$
Hint : Click to reveal hidden text
6 replies
sefatod628
Oct 28, 2024
pco
11 minutes ago
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A number theory about divisors which no one fully solved at the contest
nAalniaOMliO   19
N 13 minutes ago by Bluecloud123
Source: Belarusian national olympiad 2024
Let's call a pair of positive integers $(k,n)$ interesting if $n$ is composite and for every divisor $d<n$ of $n$ at least one of $d-k$ and $d+k$ is also a divisor of $n$
Find the number of interesting pairs $(k,n)$ with $k \leq 100$
M. Karpuk
19 replies
+2 w
nAalniaOMliO
Jul 24, 2024
Bluecloud123
13 minutes ago
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CDF of normal distribution
We2592   2
N 20 minutes ago by rchokler
Q) We know that the PDF of normal distribution of $X$ id defined by
\[ f(x) = \frac{1}{\sqrt{2\pi} \sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}} \]now what is CDF or cumulative distribution function $F_X(x)=P[X\leq x]$

how to integrate ${-\infty} \to x$
please help
2 replies
We2592
Today at 2:09 AM
rchokler
20 minutes ago
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thanks u!
Ruji2018252   0
21 minutes ago
Find all $f: \mathbb{R}\to \mathbb{R}$ and
\[f(xy)-f(x)f(y)=2022(f(x+y)-2xy-1),\forall x,y \in \mathbb{R}\]
0 replies
Ruji2018252
21 minutes ago
0 replies
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hard problem
Cobedangiu   3
N 24 minutes ago by lyllyl
problem
3 replies
1 viewing
Cobedangiu
2 hours ago
lyllyl
24 minutes ago
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Gheorghe Țițeica 2025 Grade 9 P1
AndreiVila   1
N 28 minutes ago by AlgebraKing
Source: Gheorghe Țițeica 2025
Let there be $2n+1$ distinct points on a circle. Consider the set of distances between any two out of the $2n+1$ points. What is the smallest size of this set?

Radu Bumbăcea
1 reply
AndreiVila
Yesterday at 9:06 PM
AlgebraKing
28 minutes ago
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Straightforward NT
TheMathBob   5
N 39 minutes ago by Avron
Source: Polish MO Finals P1 2023
Given a sequence of positive integers $a_1, a_2, a_3, \ldots$ such that for any positive integers $k$, $l$ we have $k+l ~ | ~ a_k + a_l$. Prove that for all positive integers $k > l$, $a_k - a_l$ is divisible by $k-l$.
5 replies
TheMathBob
Mar 29, 2023
Avron
39 minutes ago
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2025 TST 22
EthanWYX2009   0
40 minutes ago
Source: 2025 TST 22
Let \( A \) be a set of 2025 positive real numbers. For a subset \( T \subseteq A \), define \( M_T \) as the median of \( T \) when all elements of \( T \) are arranged in increasing order, with the convention that \( M_\emptyset = 0 \). Define
\[ P(A) = \sum_{\substack{T \subseteq A \\ |T| \text{ odd}}} M_T, \quad Q(A) = \sum_{\substack{T \subseteq A \\ |T| \text{ even}}} M_T. \]Find the smallest real number \( C \) such that for any set \( A \) of 2025 positive real numbers, the following inequality holds:
\[ P(A) - Q(A) \leq C \cdot \max(A), \]where \(\max(A)\) denotes the largest element in \( A \).
0 replies
1 viewing
EthanWYX2009
40 minutes ago
0 replies
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A and B play a game
EthanWYX2009   0
41 minutes ago
Source: 2025 TST 23
Let \( n \geq 2 \) be an integer. Two players, Alice and Bob, play the following game on the complete graph \( K_n \): They take turns to perform operations, where each operation consists of coloring one or two edges that have not been colored yet. The game terminates if at any point there exists a triangle whose three edges are all colored.

Prove that there exists a positive number \(\varepsilon\), Alice has a strategy such that, no matter how Bob colors the edges, the game terminates with the number of colored edges not exceeding
\[ \left( \frac{1}{4} - \varepsilon \right) n^2 + n. \]
0 replies
EthanWYX2009
41 minutes ago
0 replies
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Gheorghe Țițeica 2025 Grade 11 P1
AndreiVila   1
N 2 hours ago by Mathzeus1024
Source: Gheorghe Țițeica 2025
Find all continuous functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $f(x+y)=f(x+f(y))$ for all $x,y\in\mathbb{R}$.
1 reply
AndreiVila
Yesterday at 9:40 PM
Mathzeus1024
2 hours ago
J
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An Integral Inequality from the Chinese Internet
Blast_S1   1
N 2 hours ago by MS_asdfgzxcvb
Source: Xiaohongshu
Let $f(x)\in C[0,3]$ satisfy $f(x) \ge 0$ for all $x$ and
$$\int_0^3 \frac{1}{1 + f(x)}\,dx = 1.$$Show that
$$\int_0^3\frac{f(x)}{2 + f(x)^2}\,dx \le 1.$$
1 reply
Blast_S1
Today at 2:39 AM
MS_asdfgzxcvb
2 hours ago
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Is this true?
Entrepreneur   1
N 3 hours ago by GreenKeeper
Source: Conjectured by me
$$\color{blue}{\frac ba\cdot\frac{a+1}{b+1}\cdot\frac{b+2}{a+2}\cdot\frac{a+3}{b+3}\cdots=\frac{\Gamma(\frac a2)\Gamma(\frac{b+1}{2})}{\Gamma(\frac b2)\Gamma(\frac{a+1}{2})}.}$$
1 reply
Entrepreneur
Today at 9:08 AM
GreenKeeper
3 hours ago
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Time Scale Calculus- Dynamical inequalities
ehuseyinyigit   3
N Today at 1:10 AM by paxtonw
Does Maclaurin's Inequality have a dynamic version in time scale calculus, especially for diamond alpha calculus?
3 replies
ehuseyinyigit
Mar 23, 2025
paxtonw
Today at 1:10 AM
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Time Scale Calculus- Dynamical inequalities
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Reveal topic tags
inequalities
advanced fields
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ehuseyinyigit
790 posts
ehuseyinyigit
#1 h  Mar 23, 2025, 10:05 AM
Y by
Does Maclaurin's Inequality have a dynamic version in time scale calculus, especially for diamond alpha calculus?
Z K Y
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ehuseyinyigit
790 posts
ehuseyinyigit
#2 h  Mar 23, 2025, 11:20 AM
Y by
There exists dynamuc versions of Radon's, Jensen's and Nesbitt's Inequality, but I need MACLAURIN.
Z K Y
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ehuseyinyigit
790 posts
ehuseyinyigit
#3 h  Mar 26, 2025, 6:13 PM
Y by
Anyone??
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paxtonw
5 posts
paxtonw
#4 h  Today at 1:10 AM
Y by
Doesn't exist
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