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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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Hard NT problem
tiendat004   2
N a few seconds ago by avinashp
Given two odd positive integers $a,b$ are coprime. Consider the sequence $(x_n)$ given by $x_0=2,x_1=a,x_{n+2}=ax_{n+1}+bx_n,$ $\forall n\geq 0$. Suppose that there exist positive integers $m,n,p$ such that $mnp$ is even and $\dfrac{x_m}{x_nx_p}$ is an integer. Prove that the numerator in its simplest form of $\dfrac{m}{np}$ is an odd integer greater than $1$.
2 replies
tiendat004
Aug 15, 2024
avinashp
a few seconds ago
J
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disjoint subsets
nayel   2
N 13 minutes ago by alexanderhamilton124
Source: Taiwan 2001
Let $n\ge 3$ be an integer and let $A_{1}, A_{2},\dots, A_{n}$ be $n$ distinct subsets of $S=\{1, 2,\dots, n\}$. Show that there exists $x\in S$ such that the n subsets $A_{i}-\{x\}, i=1,2,\dots n$ are also disjoint.

what i have is this
2 replies
nayel
Apr 18, 2007
alexanderhamilton124
13 minutes ago
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Modular Arithmetic and Integers
steven_zhang123   2
N 19 minutes ago by GreekIdiot
Integers \( n, a, b \in \mathbb{Z}^+ \) satisfies \( n + a + b = 30 \). If \( \alpha < b, \alpha \in \mathbb{Z^+} \), find the maximum possible value of $\sum_{k=1}^{\alpha} \left \lfloor \frac{kn^2 \bmod a }{b-k} \right \rfloor $.
2 replies
steven_zhang123
Mar 28, 2025
GreekIdiot
19 minutes ago
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f(x+y)f(z)=f(xz)+f(yz)
dangerousliri   30
N 21 minutes ago by GreekIdiot
Source: Own
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that for all irrational numbers $x, y$ and $z$,
$$f(x+y)f(z)=f(xz)+f(yz)$$
Some stories about this problem. This problem it is proposed by me (Dorlir Ahmeti) and Valmir Krasniqi. We did proposed this problem for IMO twice, on 2018 and on 2019 from Kosovo. None of these years it wasn't accepted and I was very surprised that it wasn't selected at least for shortlist since I think it has a very good potential. Anyway I hope you will like the problem and you are welcomed to give your thoughts about the problem if it did worth to put on shortlist or not.
30 replies
dangerousliri
Jun 25, 2020
GreekIdiot
21 minutes ago
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No more topics!
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An alien statement I came across
GreekIdiot   3
N Mar 30, 2025 by GreekIdiot
Source: Some article I read a while ago, cannot find it...
Let $\mathbb{P} \subset \mathbb{N}$ be a set that intersects all non-finite integer arithmetic progressions, $\mathbb {A}$ be the set of prime divisors of $a^n-1$ and $\mathbb {B}$ be the set of prime divisors of $b^n-1$. Suppose $\mathbb {B} \subset \mathbb {A} \hspace{2 mm} \forall \hspace{2mm} n \in \mathbb{P}$. Prove that $b=a^k$, $k \in \mathbb {N}$
3 replies
GreekIdiot
Feb 15, 2025
GreekIdiot
Mar 30, 2025
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An alien statement I came across
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Reveal topic tags
Arithmetic Progression
Cyclotomic Polynomials
very hard
number theory
L
G H BBookmark kLocked kLocked NReply
Source: Some article I read a while ago, cannot find it...
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GreekIdiot
152 posts
GreekIdiot
#1 h  Feb 15, 2025, 4:31 PM
Y by
Let $\mathbb{P} \subset \mathbb{N}$ be a set that intersects all non-finite integer arithmetic progressions, $\mathbb {A}$ be the set of prime divisors of $a^n-1$ and $\mathbb {B}$ be the set of prime divisors of $b^n-1$. Suppose $\mathbb {B} \subset \mathbb {A} \hspace{2 mm} \forall \hspace{2mm} n \in \mathbb{P}$. Prove that $b=a^k$, $k \in \mathbb {N}$
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GreekIdiot
152 posts
GreekIdiot
#3 h  Feb 20, 2025, 2:58 PM
Y by
too hard?
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DVDthe1st
341 posts
DVDthe1st
#4 h  Mar 30, 2025, 1:25 AM
Y by
Certainly it is harder than this problem (which asks to show that if the set of prime divisors are equal, then $a=b$). Maybe the solution by angiland can be adapted but I'm not sure.
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GreekIdiot
152 posts
GreekIdiot
#5 h  Mar 30, 2025, 10:28 AM
Y by
Will think about it yeah
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