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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

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

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

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

Nordic 2025 P3

anirbanbz 8

Source: Nordic 2025

Let $ABC$ be an acute triangle with orthocenter $H$ and circumcenter $O$ . Let $E$ and $F$ be points on the line segments $AC$ and $AB$ respectively such that $AEHF$ is a parallelogram. Prove that $\vert OE \vert = \vert OF \vert$ .

8 replies

anirbanbz

Mar 25, 2025

Primeniyazidayi

26 minutes ago

A number theory problem from the British Math Olympiad

Rainbow1971 11

Source: British Math Olympiad, 2006/2007, round 1, problem 6

I am a little surprised to find that I am (so far) unable to solve this little problem:

[quote]Let $n$ be an integer. Show that, if $2 + 2 \sqrt{1+12n^2}$ is an integer, then it is a perfect square.[/quote]

I set $k := \sqrt{1+12n^2}$ . If $2 + 2 \sqrt{1+12n^2}$ is an integer, then $k (=\sqrt{1+12n^2})$ is at least rational, so that $1 + 12n^2$ must be a perfect square then. Using Conway's topograph method, I have found out that the smallest non-negative pairs $(n, k)$ for which this happens are $(0,1), (2,7), (28,97)$ and $(390, 1351)$ , and that, for every such pair $(n,k)$ , the "next" such pair can be calculated as
$\begin{bmatrix} 7 & 2 \\ 24 & 7 \end{bmatrix} \begin{bmatrix} n \\ k \end{bmatrix} .$ The eigenvalues of that matrix are irrational, however, so that any calculation which uses powers of that matrix is a little cumbersome. There must be an easier way, but I cannot find it. Can you?

Thank you.

11 replies

Rainbow1971

Yesterday at 8:39 PM

Rainbow1971

an hour ago

f( - f (x) - f (y))= 1 -x - y , in Zxz

parmenides51 6

Source: 2020 Dutch IMO TST 3.3

Find all functions $f: Z \to Z$ that satisfy $f(-f (x) - f (y))= 1 -x - y$ for all $x, y \in Z$

6 replies

parmenides51

Nov 22, 2020

Chikara

an hour ago

Hard limits

Snoop76 2

$a_n$ and $b_n$ satisfies the following recursion formulas: $a_{0}=1,$ $b_{0}=1$ , $a_{n+1}=a_{n}+b_{n}$ $\text{[math]}$ and $\text{[math]}$ $b_{n+1}=(2n+3)b_{n}+a_{n}$ . Find $\lim_{n \to \infty} \frac{a_n}{(2n-1)!!}$ $\text{[math]}$ and $\text{[math]}$ $\lim_{n \to \infty} \frac{b_n}{(2n+1)!!}.$

2 replies

Snoop76

Mar 25, 2025

maths_enthusiast_0001

an hour ago

College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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114,013 topics

3 users

TOPICS

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First Poster

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

1571 replies

rrusczyk

Mar 24, 2025

SmartGroot

Mar 26, 2025

k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Mar 2, 2025

0 replies

What functions check these conditions?

TheBlackPuzzle913 0

Source: RMO shortlist, Mihai Bunget and Dragoș Gabriel Borugă

Find all functions $f : \mathbb{R} \rightarrow (0, \infty)$ that are twice differentiable and satisfy $3(f'(x))^2 \le 2f(x)f''(x) , \forall x \in \mathbb{R}$

0 replies

1 viewing

TheBlackPuzzle913

6 minutes ago

0 replies

Sequence, limit and number theory

KAME06 1

Source: Ecuador National Olympiad OMEC level U 2023 P6 Day 2

A positive integers sequence is defined such that, for all $n \ge 2$ , $a_{n+1}$ is the greatest prime divisor of $a_1+a_2+...+a_n$ . Find:
$\lim_{n \rightarrow \infty} \frac{a_n}{n}$

1 reply

KAME06

Feb 6, 2025

Rainbow1971

18 minutes ago

something like MVT

mqoi_KOLA 6

If $F$ is a continuous function on $[0,1]$ such that $F(0) = F(1)$ , then there exists a $c \in (0,1)$ such that:

$F(c) = \frac{1}{c} \int_0^c F(x) \,dx$

6 replies

mqoi_KOLA

Today at 11:37 AM

Filipjack

an hour ago

nice integral

Martin.s 1

$\int_0^\infty \frac{\tanh x}{4x (1+\cosh(2x))} dx$

1 reply

Martin.s

Yesterday at 8:09 PM

Entrepreneur

2 hours ago

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Let $a, b, c$ be distinct real numbers and $x$ be a real number. Given that three numbers among
$ax^2+bx+c, ax^2+cx+b, bx^2+cx+a, bx^2+ax+c, cx^2+ax+b, cx^2+bx+a$
coincide, prove that $x=1$ .

BarisKoyuncu

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Two distinct positive integers are called "relatively consistent" if the larger one can be written as a sum of some distinct positive divisors of the other one. Show that there exist 2018 positive integers such that any two of them are "relatively consistent"

BarisKoyuncu

view topic

Let $H$ be the orthocenter of an acute angled triangle $ABC$ . Circumcircle of the triangle $ABC$ and the circle of diameter $[AH]$ intersect at point $E$ , different from $A$ . Let $M$ be the midpoint of the small arc $BC$ of the circumcircle of the triangle $ABC$ and let $N$ the midpoint of the large arc $BC$ of the circumcircle of the triangle $BHC$ Prove that points $E, H, M, N$ are concyclic.

parmenides51

view topic

$n\geq3$ boxes are placed around a circle. At the first step we choose some boxes. At the second step for each chosen box we put a ball into the chosen box and into each of its two neighbouring boxes. Find the total number of possible distinct ball distributions which can be obtained in this way. (All balls are identical.)

BarisKoyuncu

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Site Support Tech support and questions about AoPS classes and materials

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k a My Retirement & New Leadership at AoPS

rrusczyk 1571

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SmartGroot

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k a March Highlights and 2025 AoPS Online Class Information

jlacosta 0

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jlacosta

Mar 2, 2025

0 replies

How is this possible

Craftybutterfly 15

This is very wrong

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Craftybutterfly

Mar 26, 2025

Demetri

Today at 12:54 PM

Blog error

Beaniebo4 3

I was making my blog and trying to add contributors, but after pressing the checkmark, the site kept on refreshing, deleting all my blog info and not adding contributors. This happened several times.

3 replies

Beaniebo4

Today at 3:07 AM

Beaniebo4

Today at 3:42 AM

Pressing 'go down button' always creates a gray box on the last post

Craftybutterfly 21

Summary of the problem: Pressing go down to last post button always creates a gray box overlapping last post
Page URL: any forum
Steps to reproduce:
1. Go to any topic in a forum
2. The gray box at the bottom overlaps part of the first post
Expected behavior: Should not show a gray box
Frequency: 100% of the time
Operating system(s): Linux HP EliteBook 835 G8 Notebook PC
Browser(s), including version: Chrome 133.0.6943.142 (Official Build) (64-bit) (cohort: Stable)
Additional information: It works on any other device, on my iPhone XR, a MacOS, and my iPad. Took the screenshot a month ago. The gray box still appears

21 replies

Craftybutterfly

Mar 12, 2025

jlacosta

Yesterday at 11:05 PM

k They added something new on community!!!!

jb2015007 7

They added something new on community!!!!

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jb2015007

Yesterday at 9:23 PM

eg4334

Yesterday at 9:49 PM

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AIME 2025

2025 Bangladesh Mathematical Olympiad
BdMO 2025 National Round Problems

2025 Bulgarian Winter Tournament
Bulgarian Winter Tournament 2025

2025 Bundeswettbewerb Mathematik
Bundeswettbewerb Mathematik 2025

2025 Canada Junior National Olympiad
Canada Junior National Olympiad 2025

2025 Canada National Olympiad
Canada National Olympiad 2025

2025 Caucasus Mathematical Olympiad
X Caucasus Mathematical Olympiad

2025 China National Olympiad
2025 China National Olympiad

2025 China Team Selection Test
China Team Selection Test 2025

2025 Greece National Olympiad
2025 Greece National Olympiad

2025 India National Olympiad
India National Olympiad 2025

2025 India STEMS

2025 International Zhautykov Olympiad
International Zhautykov Olympiad 2025

2025 Israel National Olympiad (Gillis)
An Olympiad for grades 7-12.

2025 Israel TST

2025 Japan MO Finals
Japan MO Finals 2025

2025 Korea Winter Program Practice Test
Korea Winter Program Practice Test 2025

2025 Kyiv City MO Round 1
Problems from first round of Kyiv Mathematical Olympiad 2025

2025 Kyiv City MO Round 2
Problems from second round of Kyiv Mathematical Olympiad 2025

2025 Malaysian APMO Camp Selection Test
Malaysian APMO Camp Selection Test for APMO 2025

2025 Nordic
Nordic 2025

2025 Philippine MO

2025 Poland - First Round

2025 Poland - Second Round
Second Round - Poland 2025

2025 Romanian Master of Mathematics
15th RMM 2025

2025 Sharygin Geometry Olympiad
Sharygin Geometry Olympiad 2025

2025 Taiwan TST Round 1

2025 Taiwan TST Round 2
Taiwan TST Round 2 2025

2025 Turkey EGMO TST
Turkey EGMO TST 2025

2025 Turkey Team Selection Test
Turkey Team Selection Test 2025

2025 Ukraine National Mathematical Olympiad
Ukraine National Mathematical Olympiad 2025

2025 USA IMO Team Selection Test
USA Team Selection Test for IMO 2025

2025 USAJMO
USAJMO 2025

2025 USAMO
USAMO 2025

2025 Vietnam National Olympiad
VMO 2025

2025 Vietnam Team Selection Test
Vietnam Team Selection Test for 2025 IMO

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