Stay ahead of learning milestones! Enroll in a class over the summer!

Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/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.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

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0 replies
jlacosta
May 1, 2025
0 replies
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
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
Nice concurrency
navi_09220114   4
N 20 minutes ago by quacksaysduck
Source: TASIMO 2025 Day 1 Problem 2
Four points $A$, $B$, $C$, $D$ lie on a semicircle $\omega$ in this order with diameter $AD$, and $AD$ is not parallel to $BC$. Points $X$ and $Y$ lie on segments $AC$ and $BD$ respectively such that $BX\parallel AD$ and $CY\perp AD$. A circle $\Gamma$ passes through $D$ and $Y$ is tangent to $AD$, and intersects $\omega$ again at $Z\neq D$. Prove that the lines $AZ$, $BC$ and $XY$ are concurrent.
4 replies
navi_09220114
May 19, 2025
quacksaysduck
20 minutes ago
Numbers on a circle
navi_09220114   3
N 31 minutes ago by quacksaysduck
Source: TASIMO 2025 Day 1 Problem 1
For a given positive integer $n$, determine the smallest integer $k$, such that it is possible to place numbers $1,2,3,\dots, 2n$ around a circle so that the sum of every $n$ consecutive numbers takes one of at most $k$ values.
3 replies
1 viewing
navi_09220114
May 19, 2025
quacksaysduck
31 minutes ago
D1033 : A problem of probability for dominoes 3*1
Dattier   1
N 32 minutes ago by Dattier
Source: les dattes à Dattier
Let $G$ a grid of 9*9, we choose a little square in $G$ of this grid three times, we can choose three times the same.

What the probability of cover with 3*1 dominoes this grid removed by theses little squares (one, two or three) ?
1 reply
Dattier
May 15, 2025
Dattier
32 minutes ago
f(n)=f(n-1)+1
Seventh   9
N 2 hours ago by cursed_tangent1434
Source: Problem 3, Brazilian MO 2015
Given a natural $n>1$ and its prime fatorization $n=p_1^{\alpha 1}p_2^{\alpha_2} \cdots p_k^{\alpha_k}$, its false derived is defined by $$f(n)=\alpha_1p_1^{\alpha_1-1}\alpha_2p_2^{\alpha_2-1}...\alpha_kp_k^{\alpha_k-1}.$$Prove that there exist infinitely many naturals $n$ such that $f(n)=f(n-1)+1$.
9 replies
Seventh
Oct 20, 2015
cursed_tangent1434
2 hours ago
Functional equation meets inequality condition
Lukaluce   1
N 2 hours ago by sarjinius
Source: 2025 Macedonian Balkan Math Olympiad TST Problem 3
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ that satisfy
\[f(xf(y) + f(x)) = f(x)f(y) + 2f(x) + f(y) - 1,\]for every $x, y \in \mathbb{R}$, and $f(kx) > kf(x)$ for every $x \in \mathbb{R}$ and $k \in \mathbb{R}$, such that $k > 1$.
1 reply
Lukaluce
Apr 14, 2025
sarjinius
2 hours ago
Moving points in a plane
IAmTheHazard   2
N 2 hours ago by shanelin-sigma
Source: ELMO Shortlist 2024/C5
Let $\mathcal{S}$ be a set of $10$ points in a plane that lie within a disk of radius $1$ billion. Define a $move$ as picking a point $P \in \mathcal{S}$ and reflecting it across $\mathcal{S}$'s centroid. Does there always exist a sequence of at most $1500$ moves after which all points of $\mathcal{S}$ are contained in a disk of radius $10$?

Advaith Avadhanam
2 replies
IAmTheHazard
Jun 22, 2024
shanelin-sigma
2 hours ago
thank you !
Nakumi   0
3 hours ago
Given two non-constant polynomials $P(x),Q(x)$ such that for every real number $c$, $P(c)$ is a perfect square if and only if $Q(c)$ is a perfect square. Prove that $P(x)Q(x)$ is the square of a polynomial with real coefficients.
0 replies
Nakumi
3 hours ago
0 replies
Same divisor
sam-n   16
N 3 hours ago by AbdulWaheed
Source: IMO Shortlist 1997, Q14, China TST 2005
Let $ b, m, n$ be positive integers such that $ b > 1$ and $ m \neq n.$ Prove that if $ b^m - 1$ and $ b^n - 1$ have the same prime divisors, then $ b + 1$ is a power of 2.
16 replies
sam-n
Mar 6, 2004
AbdulWaheed
3 hours ago
sum of gcd over sets is more then sum of gcd over union
Miquel-point   3
N 3 hours ago by Jupiterballs
Source: KoMaL A. 882
Let $H_1, H_2,\ldots, H_m$ be non-empty subsets of the positive integers, and let $S$ denote their union. Prove that
\[\sum_{i=1}^m \sum_{(a,b)\in H_i^2}\gcd(a,b)\ge\frac1m \sum_{(a,b)\in S^2}\gcd(a,b).\]Proposed by Dávid Matolcsi, Berkeley
3 replies
Miquel-point
Jun 11, 2024
Jupiterballs
3 hours ago
Erasing the difference of two numbers
BR1F1SZ   5
N 3 hours ago by Jupiterballs
Source: Austria National MO Part 1 Problem 3
Consider the following game for a positive integer $n$. Initially, the numbers $1, 2, \ldots, n$ are written on a board. In each move, two numbers are selected such that their difference is also present on the board. This difference is then erased from the board. (For example, if the numbers $3,6,11$ and $17$ are on the board, then $3$ can be erased as $6 - 3=3$, or $6$ as $17 - 11=6$, or $11$ as $17 - 6=11$.)

For which values of $n$ is it possible to end with only one number remaining on the board?

(Michael Reitmeir)
5 replies
BR1F1SZ
May 5, 2025
Jupiterballs
3 hours ago
another diophantine about primes
AwesomeYRY   132
N Today at 3:23 AM by cursed_tangent1434
Source: USAMO 2022/4, JMO 2022/5
Find all pairs of primes $(p, q)$ for which $p-q$ and $pq-q$ are both perfect squares.
132 replies
AwesomeYRY
Mar 24, 2022
cursed_tangent1434
Today at 3:23 AM
for the contest high achievers, can you share your math path?
HCM2001   20
N Today at 3:22 AM by Yrock
Hi all
Just wondering if any orz or high scorers on contests at young age (which are a lot of u guys lol) can share what your math path has been like?
- school math: you probably finish calculus in 5th grade or something lol then what do you do for the rest of the school? concurrent enrollment? college class? none (focus on math competitions)?
- what grade did you get honor roll or higher on AMC 8, AMC 10, AIME qual, USAJMO qual, etc?
- besides aops do you use another program to study? (like Mr Math, Alphastar, etc)?

You're all great inspirations and i appreciate the answers.. you all give me a lot of motivation for this math journey. Thanks
20 replies
HCM2001
Yesterday at 7:50 PM
Yrock
Today at 3:22 AM
[TEST RELEASED] OMMC Year 5
DottedCaculator   103
N Today at 3:05 AM by vincentwant
Test portal: https://ommc-test-portal-2025.vercel.app/

Hello to all creative problem solvers,

Do you want to work on a fun, untimed team math competition with amazing questions by MOPpers and IMO & EGMO medalists? $\phantom{You lost the game.}$
Do you want to have a chance to win thousands in cash and raffle prizes (no matter your skill level)?

Check out the fifth annual iteration of the

Online Monmouth Math Competition!

Online Monmouth Math Competition, or OMMC, is a 501c3 accredited nonprofit organization managed by adults, college students, and high schoolers which aims to give talented high school and middle school students an exciting way to develop their skills in mathematics.

Our website: https://www.ommcofficial.org/

This is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read carefully and thoroughly. Join our Discord or monitor this thread for updates and test releases.

How hard is it?

We plan to raffle out a TON of prizes over all competitors regardless of performance. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!

How are the problems?

You can check out our past problems and sample problems here:
https://www.ommcofficial.org/sample
https://www.ommcofficial.org/2022-documents
https://www.ommcofficial.org/2023-documents
https://www.ommcofficial.org/ommc-amc

How will the test be held?/How do I sign up?

Solo teams?

Test Policy

Timeline:
Main Round: May 17th - May 24th
Test Portal Released. The Main Round of the contest is held. The Main Round consists of 25 questions that each have a numerical answer. Teams will have the entire time interval to work on the questions. They can submit any time during the interval. Teams are free to edit their submissions before the period ends, even after they submit.

Final Round: May 26th - May 28th
The top placing teams will qualify for this invitational round (5-10 questions). The final round consists of 5-10 proof questions. Teams again will have the entire time interval to work on these questions and can submit their proofs any time during this interval. Teams are free to edit their submissions before the period ends, even after they submit.

Conclusion of Competition: Early June
Solutions will be released, winners announced, and prizes sent out to winners.

Scoring:

Prizes:

I have more questions. Whom do I ask?

We hope for your participation, and good luck!

OMMC staff

OMMC’S 2025 EVENTS ARE SPONSORED BY:

[list]
[*]Nontrivial Fellowship
[*]Citadel
[*]SPARC
[*]Jane Street
[*]And counting!
[/list]
103 replies
DottedCaculator
Apr 26, 2025
vincentwant
Today at 3:05 AM
4th grader qual JMO
HCM2001   8
N Today at 2:39 AM by Yrock
i mean.. whattttt??? just found out about this.. is he on aops? (i'm sure he is) where are you orz lol..
https://www.mathschool.com/blog/results/celebrating-success-douglas-zhang-is-rsm-s-youngest-usajmo-qualifier
8 replies
HCM2001
Today at 12:53 AM
Yrock
Today at 2:39 AM
MathPath
PatTheKing806   13
N May 4, 2025 by Nora2021
Is anybody else going to MathPath?

I haven't gotten in. its been 3+ weeks since they said my application was done.
13 replies
PatTheKing806
Mar 24, 2025
Nora2021
May 4, 2025
MathPath
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PatTheKing806
1022 posts
#1 • 1 Y
Y by PikaPika999
Is anybody else going to MathPath?

I haven't gotten in. its been 3+ weeks since they said my application was done.
This post has been edited 1 time. Last edited by PatTheKing806, Mar 24, 2025, 1:30 AM
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sciencegirl25
75 posts
#2 • 2 Y
Y by PatTheKing806, PikaPika999
Hey! I've been to MathPath, last year (im not this year), and they do rolling admissions, meaning that depending on when you finished your apps. One of my friends got accepted already, because she submitted early. You should probably expect a letter soon or a waitlist since the send the letters out in batches. hope this helps!
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ZMB038
261 posts
#3 • 2 Y
Y by PikaPika999, SirAppel
Hi I'm Zoe and I'm in 6th grade. I am going to Math Path this year and I'm kinda nervous. @sciencegirl25 what is math path like? Did you go in 6th grade? What are the teachers like? Is it really hard? Is it like the application?
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SOAR1231
28 posts
#4 • 1 Y
Y by PikaPika999
i got in and i am going
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evt917
2423 posts
#5 • 1 Y
Y by PikaPika999
i got in i'm unsure but 3/4 chance

(becuz i'm really young i'm the youngest age there is plus i'm small for my age)
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eyzMath
10 posts
#6 • 1 Y
Y by PikaPika999
i might be getting in but i submitted my application kind of late
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ZMB038
261 posts
#7 • 1 Y
Y by PikaPika999
evt917 wrote:
i got in i'm unsure but 3/4 chance

(becuz i'm really young i'm the youngest age there is plus i'm small for my age)

wait how old are you? If you go maybe we could hang out. I'm also short for my age.
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BraveCobra22aops
27 posts
#8 • 2 Y
Y by littlefox_amc, PikaPika999
I got in. Does anybody have suggestions for which breakouts I should consider?
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ZMB038
261 posts
#9 • 1 Y
Y by PikaPika999
BraveCobra22aops wrote:
I got in. Does anybody have suggestions for which breakouts I should consider?
SOAR1231 wrote:
i got in and i am going

What are your names? I'm Zoe, and I'm also going to MathPath this summer.
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justJen
1957 posts
#10 • 2 Y
Y by PikaPika999, sharknavy75
BraveCobra22aops wrote:
I got in. Does anybody have suggestions for which breakouts I should consider?

First, congrats! Anyways, definitely Dr. V (literally the goat) and Silas (I think he's teaching this summer, according to our latest correspondence)'s classes. Also, take classes that aren't pure math and are more like applied math; they'll be cool (shoutout Special Relativity).
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wc31415
151 posts
#11 • 1 Y
Y by PikaPika999
dr. van cott is also really good; i took her class on ducci sequences last year
also dr. zeitz's classes are really interesting
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eyzMath
10 posts
#12
Y by
i also got in!
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Craftybutterfly
541 posts
#13
Y by
I really want to but I have piano competitions.
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Nora2021
27 posts
#14
Y by
wait... what is that???
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