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a My Retirement & New Leadership at AoPS
rrusczyk   1348
N 29 minutes ago by giselezhu
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
1348 replies
+1 w
rrusczyk
Monday at 6:37 PM
giselezhu
29 minutes ago
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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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Circumcircles intersect on AO
talkon   21
N a few seconds ago by bin_sherlo
Source: InfinityDots MO Problem 3
Let $\triangle ABC$ be an acute triangle with circumcenter $O$ and orthocenter $H$. The line through $O$ parallel to $BC$ intersect $AB$ at $D$ and $AC$ at $E$. $X$ is the midpoint of $AH$. Prove that the circumcircles of $\triangle BDX$ and $\triangle CEX$ intersect again at a point on line $AO$.

Proposed by TacH
21 replies
+1 w
talkon
Mar 28, 2017
bin_sherlo
a few seconds ago
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Cyclic Configuration Implies Isosceles
maka_moli   1
N 10 minutes ago by MathsII-enjoy
Given an acute triangle $ABC$, points $D$ and $E$ are in segments $AB$ and $AC$ respectively such that $CD \perp BE$. Let $G$ be the intersection of $CD$ and $BE$ and $F$ be the intersection of $ED$ and $BC$. If $ACGF$ is a cyclic quadrilateral prove that $|FC|=|AC|$
1 reply
maka_moli
Yesterday at 6:21 AM
MathsII-enjoy
10 minutes ago
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7^p-1 -1/p
belugacat   1
N 31 minutes ago by sky.mty
Source:
Find all prime numbers $p$ such that $\dfrac{7^{p-1}-1}{p}$ is a square of an integer.
1 reply
belugacat
Aug 11, 2024
sky.mty
31 minutes ago
J
H
tangent circles
george_54   1
N an hour ago by whwlqkd
$ABC$ is a triangle with circumcenter $(\Omega)$ and $(\omega)$ is a circle tangent to $BC$ and internally to $(\Omega).$ The tangent
from $A$ to $(\omega)$ intersects $(\Omega)$ again at $D.$ If $T, P$ are the contact points of $(\omega)$ with $BC, AD$ respectively, prove that $CT=AC\cdot PD+DC\cdot PA.$
1 reply
george_54
4 hours ago
whwlqkd
an hour ago
J
No more topics!
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J
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Vieta Jumping Unsolved(Reposted)
Eagle116   2
N Mar 24, 2025 by pco
Source: MONT, Vieta Jumping part
The question is:
Let $x_1$, $x_2$, $\dots$, $x_n$ be $n$ integers. If $k>n$ is an integer, prove that the only solution to
$$x_1^2 + x_2^2 + \dots + x_n^2 = kx_1x_2\dots x_n $$is is $x_1 = x_2 = \dots = x_n = 0$.
2 replies
Eagle116
Mar 23, 2025
pco
Mar 24, 2025
J
Vieta Jumping Unsolved(Reposted)
G H J
Reveal topic tags
algebra
polynomial
Vieta
L
G H BBookmark kLocked kLocked NReply
Source: MONT, Vieta Jumping part
The post below has been deleted. Click to close.
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Eagle116
22 posts
Eagle116
#1 h  Mar 23, 2025, 4:53 PM
Y by
The question is:
Let $x_1$, $x_2$, $\dots$, $x_n$ be $n$ integers. If $k>n$ is an integer, prove that the only solution to
$$x_1^2 + x_2^2 + \dots + x_n^2 = kx_1x_2\dots x_n $$is is $x_1 = x_2 = \dots = x_n = 0$.
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Eagle116
22 posts
Eagle116
#2 h  Mar 24, 2025, 6:41 AM
Y by
Bumping?
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
pco
23477 posts
pco
#3 h  Mar 24, 2025, 7:03 AM
Y by
Eagle116 wrote:
The question is:
Let $x_1$, $x_2$, $\dots$, $x_n$ be $n$ integers. If $k>n$ is an integer, prove that the only solution to
$$x_1^2 + x_2^2 + \dots + x_n^2 = kx_1x_2\dots x_n $$is is $x_1 = x_2 = \dots = x_n = 0$.
Wrong.
Choose as counter-example $(n,k)=(1,2)$ and $x_1=2$
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