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H
k a August Highlights and 2025 AoPS Online Class Information
jwelsh   0
Yesterday at 2:14 PM
CONGRATULATIONS to all the competitors at this year’s International Mathematical Olympiad (IMO)! The US Team took second place with 5 gold medals and 1 silver - we are proud to say that each member of the 2025 IMO team has participated in an AoPS WOOT (Worldwide Online Olympiad Training) class!

"As a parent, I'm deeply grateful to AoPS. Tiger has taken very few math courses outside of AoPS, except for a local Math Circle that doesn't focus on Olympiad math. AoPS has been one of the most important resources in his journey. Without AoPS, Tiger wouldn't be where he is today — especially considering he's grown up in a family with no STEM background at all."
— Doreen Dai, parent of IMO US Team Member Tiger Zhang

Interested to learn more about our WOOT programs? Check out the course page here or join a Free Scheduled Info Session. Early bird pricing ends August 19th!:
CodeWOOT Code Jam - Monday, August 11th
ChemWOOT Chemistry Jam - Wednesday, August 13th
PhysicsWOOT Physics Jam - Thursday, August 14th
MathWOOT Math Jam - Friday, August 15th

There is still time to enroll in our last wave of summer camps that start in August at the Virtual Campus, our video-based platform, for math and language arts! From Math Beasts Camp 6 (Prealgebra Prep) to AMC 10/12 Prep, you can find an informative 2-week camp before school starts. Plus, our math camps don’t have homework and cover cool enrichment topics like graph theory. Our language arts courses will build the foundation for next year’s challenges, such as Language Arts Triathlon for levels 5-6 and Academic Essay Writing for high school students.

Lastly, Fall is right around the corner! You can plan your Fall schedule now with classes at either AoPS Online, AoPS Academy Virtual Campus, or one of our AoPS Academies around the US. We’ve opened new Academy locations in San Mateo, CA, Pasadena, CA, Saratoga, CA, Johns Creek, GA, Northbrook, IL, and Upper West Side (NYC), New York.

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
jwelsh
Yesterday at 2:14 PM
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
J
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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
J
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Favorite Problems from the 2024-2025 School Year
djmathman   45
N 11 minutes ago by Happyllamaalways
[center]
IMAGE
[/center]

As many people (whether from the competitor side or the problem-writing side) get ready for the 2025-2026 school year, we often try to find nice and interesting problems to solve and hone our skills. Many of these problems are classics which have passed through years or generations. But this often leaves us to throw problems from recent years to the sides. While not all problems from any given year are great, there are some that do deserve praise and are undeservedly overlooked.

So let's fix this! The question: what were some of your favorite problems from competitions that occurred in the 2024-2025 school year?

Just to clarify: this is not necessarily asking for problems which you may have solved this year for practice. Instead, I'm talking about e.g. problems which came from contests hosted within the past 12 months - so for example AMC/AIME/USA(J)MO, ARML, PUMaC, HMMT, CMIMC, CHMMC, Duke, etc., as well as any national olympiads or TST's from this year. (2024 ISL problems also count since they were released to the public in 2025.) Problems from mocks released this year are eligible, too. Also, to make things easier to read, I highly recommend writing the original problem statements in your posts, as opposed to just stating the sources.

I also think this is a good way to officially end the 2024-2025 school year of contests. :)

I'm interested in seeing what some of your responses are!
45 replies
djmathman
Jul 23, 2025
Happyllamaalways
11 minutes ago
J
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Equal segments with humpty and dumpty points.
Kratsneb   1
N 23 minutes ago by aqwxderf
Let $X$, $Y$ be such points on sides $AB$, $AC$ of a triangle $ABC$ that $BXYC$ is cyclic. $BY \cap CX = D$, $N$ is the midpoint of $AD$. In triangles $BDX$ and $CDY$ let $P$, $Q$ be the $D$-humpty points and let $S$, $T$ be the $D$-dumpty points. Prove that $AP = AQ$ and $NS = NT$.
IMAGE
1 reply
Kratsneb
4 hours ago
aqwxderf
23 minutes ago
J
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Multivariate polynomial must vanish on all permutations
DottedCaculator   2
N 24 minutes ago by CANBANKAN
Source: 2025 ELMO Shortlist A4
Fix positive integers $n$ and $k$ with $n \geq k$. Determine the smallest positive integer $d$ satisfying the following condition:

For any (not necessarily distinct) real numbers $a_1$, $\dots$, $a_n$, there exists a real-coefficient polynomial $f$ in $k$ variables satisfying the following properties:
[list]
[*] $f$ has degree at most $d$;
[*] $f$ is not identically $0$;
[*] for any permutation $b_1, \ldots, b_n$ of $a_1, \ldots, a_n$, the equation $f(b_1, \ldots, b_k) = 0$ holds.
[/list]

Benny Wang
2 replies
DottedCaculator
Jun 30, 2025
CANBANKAN
24 minutes ago
J
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Plz help with this problem question
perfectling   4
N 27 minutes ago by wisewigglyjaguar
What is the probability that a randomly selected three-digit number has the property that one digit is equal to the product of the other two? Express your answer as a common fraction.

I have tried so many ways but i still cant figure this out
4 replies
perfectling
an hour ago
wisewigglyjaguar
27 minutes ago
J
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five digit multiplication?
fruitmonster97   52
N 34 minutes ago by Nonecludiangeofan
Source: 2024 AMC 10A #1/AMC 12A #1
What is the value of $9901\cdot101-99\cdot10101?$

$\textbf{(A) }2\qquad\textbf{(B) }20\qquad\textbf{(C) }21\qquad\textbf{(D) }200\qquad\textbf{(E) }2020$
52 replies
fruitmonster97
Nov 7, 2024
Nonecludiangeofan
34 minutes ago
J
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one problem from Mathworks 2023 contest
Carmen8102   2
N 36 minutes ago by Carmen8102
Source: Mathworks math contest 2023
The letters A and B represent different digits. The 5-digit integer AB5AB = X^3-3X^2 for some two-digit integer X. Find X.

Is there a faster way of solving this problem, not trying so many numbers?
2 replies
Carmen8102
Jul 30, 2025
Carmen8102
36 minutes ago
J
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Combinatorics
slimshady360   0
an hour ago
Source: IMO 2005-Problem 6.
Does anybody have any idea how to solve this with graph theory?
0 replies
slimshady360
an hour ago
0 replies
J
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USAMO 2003 Problem 1
MithsApprentice   75
N an hour ago by SomeonecoolLovesMaths
Prove that for every positive integer $n$ there exists an $n$-digit number divisible by $5^n$ all of whose digits are odd.
75 replies
MithsApprentice
Sep 27, 2005
SomeonecoolLovesMaths
an hour ago
J
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Some of my less-seen proposals
navid   7
N an hour ago by shaboon
Dear friends,

Since 2003, I have had several nice days in AOPS-- i.e., Mathlinks; as some of you may remember. I decided to share you some of my less-seen proposals. Some of them may be considered as some early ethudes; several of them already appeared on some competitions or journals. I hope you like them and this be a good starting point for working on them. Please take a look at the following link.

https://drive.google.com/file/d/1bntcjZAHZ-WN1lfGbNbz0uyFvhBTMEhz/view?usp=sharing

Best regards,
Navid.
7 replies
navid
Jul 30, 2025
shaboon
an hour ago
J
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Ugly functional equation
Taha1381   11
N an hour ago by shaboon
Source: Iranian third round 2019 Finals algebra exam problem 3
Let $a,b,c$ be non-zero distinct real numbers so that there exist functions $f,g:\mathbb{R}^{+} \to \mathbb{R}$ so that:

$af(xy)+bf(\frac{x}{y})=cf(x)+g(y)$

For all positive real $x$ and large enough $y$.

Prove that there exists a function $h:\mathbb{R}^{+} \to \mathbb{R}$ so that:

$f(xy)+f(\frac{x}{y})=2f(x)+h(y)$

For all positive real $x$ and large enough $y$.
11 replies
Taha1381
Aug 18, 2019
shaboon
an hour ago
J
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Bicentric Quadrilateral Concurrence
anantmudgal09   2
N 2 hours ago by MathLuis
Source: India-Iran-Singapore-Taiwan Friendly Contest 2025 Problem 2
Let $ABCD$ be a quadrilateral with both an incircle and a circumcircle. Let $I$ and $O$ be the incenter and circumcenter of $ABCD$, respectively. Let $E$ be the intersection of lines $AB$ and $CD$, and let $F$ be the intersection of lines $BC$ and $DA$. Let $X$ and $Y$ be the intersections of the line $FI$ with lines $AB$ and $CD$, respectively. Prove that the circumcircle of $\triangle EIF$, the circumcircle of $\triangle EXY$, and the line $FO$ are concurrent.
2 replies
anantmudgal09
Today at 7:15 AM
MathLuis
2 hours ago
J
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find all continuous functions
aktyw19   3
N 2 hours ago by jasperE3
Find all continuous functions $f:\mathbb{R}\to\mathbb{R}$ such that $f(xy)+f(x+y)=f(xy+x)+f(y)$.
3 replies
aktyw19
Sep 28, 2013
jasperE3
2 hours ago
J
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Find all functions
aktyw19   2
N 2 hours ago by jasperE3
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that
$f(x^2+y^2)=f(f(x))+f(xy)+f(f(y))$ $\forall x, y\in\mathbb{R}$
2 replies
aktyw19
Mar 27, 2014
jasperE3
2 hours ago
J
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intersting problem
teomihai   2
N 2 hours ago by teomihai
Prove $\frac{1}{5n+1}+\frac{1}{5n+2}+...+\frac{1}{10n}>\frac{3}{5} $ for any $n>0$,integer .
2 replies
teomihai
2 hours ago
teomihai
2 hours ago
J
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J
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query about computing for summer program application psets
Possible   2
N Feb 28, 2025 by Yiyj1
Hello AoPSers,

I am applying for PROMYS this year. For some of the problems in the application problem set, I have considered writing out some code to I can notice certain patterns within smaller test cases more efficiently. Would this be acceptable as long as I include mathematical justification?

Best, Possible
2 replies
Possible
Feb 25, 2025
Yiyj1
Feb 28, 2025
J
query about computing for summer program application psets
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Reveal topic tags
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Possible
6508 posts
Possible
#1 h  Feb 25, 2025, 5:26 AM
Y by
Hello AoPSers,

I am applying for PROMYS this year. For some of the problems in the application problem set, I have considered writing out some code to I can notice certain patterns within smaller test cases more efficiently. Would this be acceptable as long as I include mathematical justification?

Best, Possible
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Magnetoninja
283 posts
Magnetoninja
#3 h  Feb 28, 2025, 5:32 AM
Y by
^ bump I need this answered too
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Yiyj1
1300 posts
Yiyj1
#4 h  Feb 28, 2025, 5:38 AM
Y by
I think this would be acceptable as long as you give mathematical justification. I think it's just to use a code to find the answer and to not find any mathematical justification that's not allowed. You don't really have to include the fact that you used a code, though. Just list out the test cases you tested.

Hope that helped :)
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