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k a My Retirement & New Leadership at AoPS
rrusczyk   1573
N Yesterday at 11:40 PM 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
1573 replies
rrusczyk
Mar 24, 2025
SmartGroot
Yesterday at 11:40 PM
J
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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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Inequality with factorial !
Virgil Nicula   2
N 8 minutes ago by Snoop76
Prove that for any $ n\in N^{*}$we have $ \boxed{\ \left(\frac{n}{n+1}\right)^{n+1}<\sqrt [n+1]{(n+1) !}-\sqrt [n]{n!}\ }$
2 replies
Virgil Nicula
Sep 18, 2007
Snoop76
8 minutes ago
J
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Help me...
PrimeSol   0
34 minutes ago
Please help me, someone who knows what the Lin-Phoong inequality is?
0 replies
2 viewing
PrimeSol
34 minutes ago
0 replies
J
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concyclic wanted, 2 circles tangent to incircle related
parmenides51   7
N 36 minutes ago by Ihatecombin
Source: Hong Kong TST - HKTST 2024 1.6
Let $\Omega$ be the incircle of $\Delta ABC$. There are two smaller circles $\omega_1$ amd $\omega_2$ inside $\Delta ABC$. The circle $\omega_1$ is tangent to $\Omega$ at $P$, tangent to $BC$ at $D$, and also tangent to $AB$. The circle $\omega_2$ is tangent to $\Omega$ at $Q$, tangent to $BC$ at $E$, and also tangent to $AC$. Prove that $D,E,Q,P$ are concyclic.
7 replies
parmenides51
Jul 20, 2024
Ihatecombin
36 minutes ago
J
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Number Theory Problem in Taiwan TST
chengbilly   1
N 42 minutes ago by vi144
Source: 2025 Taiwan TST Round 2 Independent Study 2-N
Find all prime number pairs $(p, q)$ such that \[p^q+q^p+p+q-5pq\]is a perfect square.

Proposed by chengbilly
1 reply
chengbilly
3 hours ago
vi144
42 minutes ago
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Inequality
Tendo_Jakarta   0
an hour ago
Let \(a,b,c\) be positive numbers such that \(a+b+c = 3\). Find the maximum value of
\[T = \dfrac{bc}{\sqrt{a}+3}+\dfrac{ca}{\sqrt{b}+3}+\dfrac{ab}{\sqrt{c}+3} \]
0 replies
Tendo_Jakarta
an hour ago
0 replies
J
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Geometry Problem in Taiwan TST
chengbilly   2
N 2 hours ago by Li4
Source: 2025 Taiwan TST Round 2 Independent Study 2-G
Given a triangle $ABC$ with circumcircle $\Gamma$, and two arbitrary points $X, Y$ on $\Gamma$. Let $D$, $E$, $F$ be points on lines $BC$, $CA$, $AB$, respectively, such that $AD$, $BE$, and $CF$ concur at a point $P$. Let $U$ be a point on line $BC$ such that $X$, $Y$, $D$, $U$ are concyclic. Similarly, let $V$ be a point on line $CA$ such that $X$, $Y$, $E$, $V$ are concyclic, and let $W$ be a point on line $AB$ such that $X$, $Y$, $F$, $W$ are concyclic. Prove that $AU$, $BV$, $CW$ concur at a single point.

Proposed by chengbilly
2 replies
chengbilly
3 hours ago
Li4
2 hours ago
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Something nice
KhuongTrang   24
N 2 hours ago by Nguyenhuyen_AG
Source: own
Problem. Given $a,b,c$ be non-negative real numbers such that $ab+bc+ca=1.$ Prove that

$$\sqrt{a+1}+\sqrt{b+1}+\sqrt{c+1}\le 1+2\sqrt{a+b+c+abc}.$$
24 replies
KhuongTrang
Nov 1, 2023
Nguyenhuyen_AG
2 hours ago
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a+b+c=3 inequality
jokehim   0
2 hours ago
Source: my problem
Let $a,b,c\ge 0: a+b+c=3.$ Prove that $$a\sqrt{bc+3}+b\sqrt{ca+3}+c\sqrt{ab+3}\ge \sqrt{12(ab+bc+ca)}.$$
0 replies
jokehim
2 hours ago
0 replies
J
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Incenter perpendiculars and angle congruences
math154   83
N 2 hours ago by Ilikeminecraft
Source: ELMO Shortlist 2012, G3
$ABC$ is a triangle with incenter $I$. The foot of the perpendicular from $I$ to $BC$ is $D$, and the foot of the perpendicular from $I$ to $AD$ is $P$. Prove that $\angle BPD = \angle DPC$.

Alex Zhu.
83 replies
math154
Jul 2, 2012
Ilikeminecraft
2 hours ago
J
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An inequality about a^3+b^3+c^3+2abc=5
JK1603JK   1
N 2 hours ago by JK1603JK
Source: unknown
Prove that
a+b+c\ge 2\left(\frac{a}{a+1}+\frac{b}{b+1}+\frac{c}{c+1}\right)

holds \forall a,b,c\ge 0: a^3+b^3+c^3+2abc=5.
1 reply
JK1603JK
Mar 25, 2025
JK1603JK
2 hours ago
J
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Bisectors, perpendicularity and circles
JuanDelPan   14
N 3 hours ago by Ilikeminecraft
Source: Pan-American Girls’ Mathematical Olympiad 2022, Problem 3
Let $ABC$ be an acute triangle with $AB< AC$. Denote by $P$ and $Q$ points on the segment $BC$ such that $\angle BAP = \angle CAQ < \frac{\angle BAC}{2}$. $B_1$ is a point on segment $AC$. $BB_1$ intersects $AP$ and $AQ$ at $P_1$ and $Q_1$, respectively. The angle bisectors of $\angle BAC$ and $\angle CBB_1$ intersect at $M$. If $PQ_1\perp AC$ and $QP_1\perp AB$, prove that $AQ_1MPB$ is cyclic.
14 replies
JuanDelPan
Oct 27, 2022
Ilikeminecraft
3 hours ago
J
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Prove angles are equal
BigSams   50
N 3 hours ago by Ilikeminecraft
Source: Canadian Mathematical Olympiad - 1994 - Problem 5.
Let $ABC$ be an acute triangle. Let $AD$ be the altitude on $BC$, and let $H$ be any interior point on $AD$. Lines $BH,CH$, when extended, intersect $AC,AB$ at $E,F$ respectively. Prove that $\angle EDH=\angle FDH$.
50 replies
BigSams
May 13, 2011
Ilikeminecraft
3 hours ago
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PD _|_ BC
parmenides51   2
N 3 hours ago by Ihatecombin
Source: Hong Kong TST - HKTST 2024 1.3
Given $\Omega ABC$ with $AB<AC$, let $AD$ be the bisector of $\angle BAC$ with $D$ on the side $BC$. Let $\Gamma$ be a circle passing through $A$ and $D$ which is tangent to $BC$ at $D$. Suppose $\Gamma$ cuts the side $AB$ again at $E\ne A$. The tangent to the circumcircle of $\Delta BDE$ at $D$ intersects $\Gamma$ again at $F\ne D$. Let $P$ be the intersection point of the segments $EF$ and $AC$. Prove that $PD$ is perpendicular to $BC$.
2 replies
parmenides51
Jul 20, 2024
Ihatecombin
3 hours ago
J
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IRAN national math olympiad(3rd round)-2010-NT exam-p6
goodar2006   4
N 3 hours ago by john0512
$g$ and $n$ are natural numbers such that $gcd(g^2-g,n)=1$ and $A=\{g^i|i \in \mathbb N\}$ and $B=\{x\equiv (n)|x\in A\}$(by $x\equiv (n)$ we mean a number from the set $\{0,1,...,n-1\}$ which is congruent with $x$ modulo $n$). if for $0\le i\le g-1$
$a_i=|[\frac{ni}{g},\frac{n(i+1)}{g})\cap B|$
prove that $g-1|\sum_{i=0}^{g-1}ia_i$.( the symbol $|$ $|$ means the number of elements of the set)($\frac{100}{6}$ points)

the exam time was 4 hours
4 replies
goodar2006
Aug 9, 2010
john0512
3 hours ago
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D1018 : Can you do that ?
Dattier   1
N Tuesday at 9:27 AM by Dattier
Source: les dattes à Dattier
We can find $A,B,C$, such that $\gcd(A,B)=\gcd(C,A)=\gcd(A,2)=1$ and $$\forall n \in \mathbb N^*, (C^n \times B \mod A) \mod 2=0 $$.

For example :

$C=20$
$A=47650065401584409637777147310342834508082136874940478469495402430677786194142956609253842997905945723173497630499054266092849839$

$B=238877301561986449355077953728734922992395532218802882582141073061059783672634737309722816649187007910722185635031285098751698$

Can you find $A,B,C$ such that $A>3$ is prime, $C,B \in (\mathbb Z/A\mathbb Z)^*$ with $o(C)=(A-1)/2$ and $$\forall n \in \mathbb N^*, (C^n \times B \mod A) \mod 2=0 $$?
1 reply
Dattier
Mar 24, 2025
Dattier
Tuesday at 9:27 AM
J
D1018 : Can you do that ?
G H J
Reveal topic tags
arithmetic
number theory
L
G H BBookmark kLocked kLocked NReply
Source: les dattes à Dattier
The post below has been deleted. Click to close.
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Dattier
1472 posts
Dattier
#1 h  Mar 24, 2025, 6:01 AM
Y by
We can find $A,B,C$, such that $\gcd(A,B)=\gcd(C,A)=\gcd(A,2)=1$ and $$\forall n \in \mathbb N^*, (C^n \times B \mod A) \mod 2=0 $$.

For example :

$C=20$
$A=47650065401584409637777147310342834508082136874940478469495402430677786194142956609253842997905945723173497630499054266092849839$

$B=238877301561986449355077953728734922992395532218802882582141073061059783672634737309722816649187007910722185635031285098751698$

Can you find $A,B,C$ such that $A>3$ is prime, $C,B \in (\mathbb Z/A\mathbb Z)^*$ with $o(C)=(A-1)/2$ and $$\forall n \in \mathbb N^*, (C^n \times B \mod A) \mod 2=0 $$?
Z K Y
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Dattier
1472 posts
Dattier
#2 h  Tuesday at 9:27 AM
Y by
No one.?
Z K Y
N Quick Reply
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