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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
+1 w
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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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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Range of solutions to the log equation
obihs   0
28 minutes ago
Source: Own
Let $n$ be a positive integer, and consider the equation:
$$(\log x)^n - x + 1 = 0\quad\cdots(\heartsuit)$$Answer the following questions. You may assume that $2.7<e<2.72$ is known.

$(1)\quad$ Determine the number of real solutions of equation $(\heartsuit)$ for each $n$.

$(2)\quad$ For $n\ge 3$ , let $r_n$ be the segond largest real solution of $(\heartsuit)$.

$(\i)\quad$ Find $\alpha$ such that $\lim_{n\to\infty} r_n =\alpha.$

$(\i\i)\quad$ Find $\lfloor\beta\rfloor$, where $\beta$ is defined as

$$\lim_{n\to\infty}n(r_n-\alpha)=\beta.$$
0 replies
obihs
28 minutes ago
0 replies
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Unsolved NT, 3rd time posting
GreekIdiot   6
N 33 minutes ago by GreekIdiot
Source: own
Solve $5^x-2^y=z^3$ where $x,y,z \in \mathbb Z$
Hint
6 replies
GreekIdiot
Mar 26, 2025
GreekIdiot
33 minutes ago
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Need hint:''(
Buh_-1235   0
34 minutes ago
Source: Canada Winter mock 2015
Recall that for any positive integer m, φ(m) denotes the number of positive integers less than m which are relatively
prime to m. Let n be an odd positive integer such that both φ(n) and φ(n + 1) are powers of two. Prove n + 1 is power
of two or n = 5.
0 replies
Buh_-1235
34 minutes ago
0 replies
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inequalities
Cobedangiu   0
36 minutes ago
Source: own
$a,b>0$ and $a+b=1$. Find min P:
$P=\sqrt{\frac{1-a}{1+7a}}+\sqrt{\frac{1-b}{1+7b}}$
0 replies
Cobedangiu
36 minutes ago
0 replies
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Gut inequality
giangtruong13   1
N 44 minutes ago by arqady
Let $a,b,c>0$ satisfy that $a+b+c=3$. Find the minimum $$\sum_{cyc} \sqrt[4]{\frac{a^3}{b+c}}$$
1 reply
giangtruong13
3 hours ago
arqady
44 minutes ago
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Minimize Expression Over Permutation
amuthup   37
N an hour ago by mananaban
Source: 2021 ISL A3
For each integer $n\ge 1,$ compute the smallest possible value of \[\sum_{k=1}^{n}\left\lfloor\frac{a_k}{k}\right\rfloor\]over all permutations $(a_1,\dots,a_n)$ of $\{1,\dots,n\}.$

Proposed by Shahjalal Shohag, Bangladesh
37 replies
amuthup
Jul 12, 2022
mananaban
an hour ago
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Let's Invert Some
Shweta_16   8
N an hour ago by ihategeo_1969
Source: STEMS 2020 Math Category B/P4 Subjective
In triangle $\triangle{ABC}$ with incenter $I$, the incircle $\omega$ touches sides $AC$ and $AB$ at points $E$ and $F$, respectively. A circle passing through $B$ and $C$ touches $\omega$ at point $K$. The circumcircle of $\triangle{KEC}$ meets $BC$ at $Q \neq C$. Prove that $FQ$ is parallel to $BI$.

Proposed by Anant Mudgal
8 replies
Shweta_16
Jan 26, 2020
ihategeo_1969
an hour ago
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very cute geo
rafaello   2
N an hour ago by ihategeo_1969
Source: MODSMO 2021 July Contest P7
Consider a triangle $ABC$ with incircle $\omega$. Let $S$ be the point on $\omega$ such that the circumcircle of $BSC$ is tangent to $\omega$ and let the $A$-excircle be tangent to $BC$ at $A_1$. Prove that the tangent from $S$ to $\omega$ and the tangent from $A_1$ to $\omega$ (distinct from $BC$) meet on the line parallel to $BC$ and passing through $A$.
2 replies
rafaello
Oct 26, 2021
ihategeo_1969
an hour ago
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Inspired by old results
sqing   3
N an hour ago by xytunghoanh
Source: Own
Let $ a, b,c\geq 0 $ and $ a+2b+3c= 2(\sqrt{6}-1).$ Prove that
$$a+ab+abc\leq 3$$Let $ a, b,c\geq 0 $ and $ a+2b+3c= 2\sqrt{6}-1.$ Prove that
$$a+ab+abc\leq \frac{25}{8}+\sqrt{ \frac{3}{2}}$$Let $ a, b,c\geq 0 $ and $ a+2b+3c= 2\sqrt{3}-1.$ Prove that
$$a+ab+abc\leq \frac{13}{8}+\frac{\sqrt{ 3}}{2}$$
3 replies
sqing
5 hours ago
xytunghoanh
an hour ago
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Power Of Factorials
Kassuno   178
N an hour ago by Maximilian113
Source: IMO 2019 Problem 4
Find all pairs $(k,n)$ of positive integers such that \[ k!=(2^n-1)(2^n-2)(2^n-4)\cdots(2^n-2^{n-1}). \]Proposed by Gabriel Chicas Reyes, El Salvador
178 replies
Kassuno
Jul 17, 2019
Maximilian113
an hour ago
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Olympiad problem - I can't solve it pls help
kjhgyuio   6
N an hour ago by GreekIdiot
Source: smo 2016
It is given that x and y are positive integers such that x>y and
√x + √y=√2000
How many different possible values can x take?
6 replies
kjhgyuio
Today at 11:07 AM
GreekIdiot
an hour ago
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Strange limit
Snoop76   4
N 2 hours ago by Svyatoslav
Find: $\lim_{n \to \infty} n\cdot\sum_{k=1}^n \frac 1 {k(n-k)!}$
4 replies
Snoop76
Mar 29, 2025
Svyatoslav
2 hours ago
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Improper integrahl manipulation
MetaphysicalWukong   1
N 2 hours ago by HacheB2031
Given the image, find out with justification if the following integrals converge or are uncertain to converge:
$\int _1^{\infty }\:\frac{h\left(x\right)}{x}dx,\:\int _1^{\infty \:}\:\sqrt{h\left(x\right)}dx,\:\int _1^{\infty \:}\:h\left(x^2\right)dx$
1 reply
MetaphysicalWukong
Today at 7:09 AM
HacheB2031
2 hours ago
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n->inf, f(n)->0
Alidq   2
N 3 hours ago by Alidq
I have a sequence $a_n=\sqrt[n]{f(n)} , n \geq 2$ where $f$ is a bijection from $\{0,1,2,….,n\}$ to itself.I need to find the limit of this sequence when $n$ tends to infinity , in the solution my friend gave to me he said that it’s trivial that the limit is greater or equal than 1 can someone tell me why?
2 replies
Alidq
3 hours ago
Alidq
3 hours ago
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Matrix in terms of exp
RenheMiResembleRice   1
N Mar 29, 2025 by Mathzeus1024
$\begin{pmatrix}X\left(t\right)\\ Y\left(t\right)\end{pmatrix}=\begin{pmatrix}\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{pmatrix}\begin{pmatrix}x\left(t\right)\\ y\left(t\right)\end{pmatrix}$

$X\left(t\right)=a_1e^t+a_2e^{-t}+a_3$
Find $a_1$, $a_2$, and $a_3$.
1 reply
RenheMiResembleRice
Mar 29, 2025
Mathzeus1024
Mar 29, 2025
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Matrix in terms of exp
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Reveal topic tags
linear algebra
matrix
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RenheMiResembleRice
255 posts
RenheMiResembleRice
#1 h  Mar 29, 2025, 3:05 AM
Y by
$\begin{pmatrix}X\left(t\right)\\ Y\left(t\right)\end{pmatrix}=\begin{pmatrix}\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{pmatrix}\begin{pmatrix}x\left(t\right)\\ y\left(t\right)\end{pmatrix}$

$X\left(t\right)=a_1e^t+a_2e^{-t}+a_3$
Find $a_1$, $a_2$, and $a_3$.
This post has been edited 3 times. Last edited by RenheMiResembleRice, Mar 29, 2025, 4:05 AM
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The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Mathzeus1024
774 posts
Mathzeus1024
#2 h  Mar 29, 2025, 4:20 PM
Y by
RenheMiResembleRice wrote:
$\begin{pmatrix}X\left(t\right)\\ Y\left(t\right)\end{pmatrix}=\begin{pmatrix}\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{pmatrix}\begin{pmatrix}x\left(t\right)\\ y\left(t\right)\end{pmatrix}$

$X\left(t\right)=a_1e^t+a_2e^{-t}+a_3$
Find $a_1$, $a_2$, and $a_3$.

Question: Are $X(t),Y(t)$ derivatives with respect to $t$?
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