High School Olympiads
Regional, national, and international math olympiads
Regional, national, and international math olympiads
3
M
G
BBookmark
VNew Topic
kLocked
High School Olympiads
Regional, national, and international math olympiads
Regional, national, and international math olympiads
3
M
G
BBookmark
VNew Topic
kLocked
No tags match your search
Minduction
algebra
combinatorics
geometry
inequalities
number theory
IMO
articles
inequalities proposed
function
algebra unsolved
circumcircle
trigonometry
number theory unsolved
inequalities unsolved
polynomial
geometry unsolved
geometry proposed
combinatorics unsolved
number theory proposed
functional equation
algebra proposed
modular arithmetic
induction
geometric transformation
incenter
calculus
3D geometry
combinatorics proposed
quadratics
Inequality
reflection
ratio
logarithms
prime numbers
analytic geometry
floor function
angle bisector
search
parallelogram
integration
Diophantine equation
rectangle
LaTeX
limit
complex numbers
probability
graph theory
conics
Euler
cyclic quadrilateral
No tags match your search
MG
Topic
First Poster
Last Poster
Proof Writing Help
gulab_jamun 1
N
3 hours ago
by Gavin_Deng
Ok so like, i'm working on proofs, and im prolly gonna use this page for any questions. My question as of now is what can I cite? Like for example, if for a question I use Evan Chen's fact 5, in my proof do I have to prove fact 5 all over again or can i say "this result follows from Evan Chen's fact 5"?
1 reply
for the contest high achievers, can you share your math path?
HCM2001 30
N
3 hours ago
by mhgelgi
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
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
30 replies

Convolution of order f(n)
trumpeter 76
N
4 hours ago
by ray66
Source: 2019 USAMO Problem 1
Let
be the set of positive integers. A function
satisfies the equation
for all positive integers
. Given this information, determine all possible values of
.
Proposed by Evan Chen


![\[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]](http://latex.artofproblemsolving.com/2/e/7/2e73ff2f75b103e9d6a4004a42e4ed7f4ee64a67.png)


Proposed by Evan Chen
76 replies
9 USAMO/JMO
BAM10 26
N
Today at 1:36 PM
by neeyakkid23
I mock ~90-100 on very recent AMC 10 mock right now. I plan to take AMC 10 final fives(9th), intermediate NT(9th), aime A+B courses in 10th and 11th and maybe mathWOOT 1 (12th). For more info I got 20 on this years AMC 8 with 3 sillies and 32 on MATHCOUNTS chapter. Also what is a realistic timeline to do this
26 replies

[TEST RELEASED] OMMC Year 5
DottedCaculator 110
N
Today at 12:14 PM
by PikaPika999
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?
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]
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?

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 designed OMMC to be accessible to beginners but also challenging to experts. Earlier questions on the main round will be around the difficulty of easy questions from the AMC 8 and AMC 10/12, and later questions will be at the difficulty of the hardest questions from the AIME. Our most skilled teams are invited to compete in an invitational final round consisting of difficult proof questions. We hope that teams will have fun and think deeply about the problems on the test, no matter their skill level.
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?
Only the best problems by our panel of dedicated and talented problem writers have been selected. Hundreds upon hundreds of problems have been comprehensively reviewed by our panel of equally wonderful testsolvers. Our content creation staff has achieved pretty much every mathematical achievement possible! Staff members have attended MOP, participated in MIT-PRIMES, RSI, SPARC, won medals at EGMO, IMO, RMM, etc. Our staff members have contributed to countless student-led math organizations and competitions in the past and we all have a high degree of mathematical experience under our belts. We believe OMMC Year 5 contains some of our best work thus far.
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?
We highly recommend competitors join our Community Discord for the latest updates on the competition, as well as for finding team members to team up with. Each team is between 1 and 4 people, inclusive. Each competitor in a team has to be 18 or younger. You won’t have to sign up right now. Look out for a test portal link by which teams can register and access the test. Teams will put in their registration information as they submit the test.
However, we do encourage you to “sign up” on this thread, just like how you might with a mock contest. This isn’t required to take the test nor does it force you to take the test. But it’s a great way to show support and bump the thread to the top of the forums, so we appreciate it. (Also a great way to find teammates!)
However, we do encourage you to “sign up” on this thread, just like how you might with a mock contest. This isn’t required to take the test nor does it force you to take the test. But it’s a great way to show support and bump the thread to the top of the forums, so we appreciate it. (Also a great way to find teammates!)
Solo teams?
Solo participants are allowed and will be treated simply as one man teams. They will be eligible for the same prizes as teams with multiple people.
Test Policy
Our test will be held completely online and untimed. We do not allow the use of anything other than writing utensils, scratch paper, compass, ruler/straightedge, and a single four function calculator (addition, subtraction, multiplication, division).
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:
For the main round, there are 25 computational (number answer questions). Each of the 25 questions will be worth 2 points, for a total of 50 points. Ties are broken by the last (highest numbered) question that one team solved and the other team didn’t, MATHCOUNTS-style. The team that solved this question would be given preference. For example, if teams A and B both have scores of 24, but Team A got question 20 wrong and Team B got question 25 wrong, then team A will be given preference over team B because team A solved question 25.
The top ~10-15 teams will move onto the final round, where there are 5-10 proof questions. Each of the questions is worth a different number of points (the specific weighting will be given to each of the finalist teams). The Olympiad round in total will be worth 50 points. A team’s total OMMC index will be the sum of the main round score and the final round score (out of 50+50=100), and teams will be ranked on their OMMC index (if there are ties, they will be broken by the aforementioned main round tie breaking system).
The top ~10-15 teams will move onto the final round, where there are 5-10 proof questions. Each of the questions is worth a different number of points (the specific weighting will be given to each of the finalist teams). The Olympiad round in total will be worth 50 points. A team’s total OMMC index will be the sum of the main round score and the final round score (out of 50+50=100), and teams will be ranked on their OMMC index (if there are ties, they will be broken by the aforementioned main round tie breaking system).
Prizes:
Prize List So Far:
- TBD
In past years we’ve received $5000+ in prizes. Stay tuned for more details, but we intend to give prizes to all teams on the leaderboard, as well as raffle out a TON of prizes over all competitors. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!
- TBD
In past years we’ve received $5000+ in prizes. Stay tuned for more details, but we intend to give prizes to all teams on the leaderboard, as well as raffle out a TON of prizes over all competitors. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!
I have more questions. Whom do I ask?
We respond most quickly on our community discord, but you can also contact us through email via the ommcofficial@gmail.com address.
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]
110 replies
Proof-based math
imbadatmath1233 5
N
Today at 3:19 AM
by LearnMath_105
Okay, I need help in deciding on how i am going to prep. My JMO index was 121.5+11 = 231.5(10A) and I missed the cutoff by 1.5. Ive already grieved about this before but I need some help in deciding what I should do next year. I think I can make JMO but my goal is to get 21+ on JMO. However, OTIS applications are already done so does anyone have any other tips on how to prep for JMO. Any help would be very much appreciated. Also, how much time should i spend on computational if i want to prep for olympiad but I don't want to get rusty. Thanks for helping!
5 replies
Awesome Math Rec Letter
cowstalker 0
Today at 12:18 AM
Hello, I recently looked at the MIT Primes website and saw that they accept recommendation letters from the Awesome Math Summer Program. Has anyone ever gotten a recommendation letter from one of the teachers in Awesome Math? I'm also planning to take AMSP and would like to get a rec letter from my teacher, too, so I was wondering if this is even possible or not.
0 replies

Circles, Lines, Angles, Oh My!
atmchallenge 19
N
Yesterday at 10:47 PM
by kilobyte144
Source: 2016 AMC 8 #23
Two congruent circles centered at points
and
each pass through the other circle's center. The line containing both
and
is extended to intersect the circles at points
and
. The circles intersect at two points, one of which is
. What is the degree measure of
?









19 replies
another diophantine about primes
AwesomeYRY 133
N
Yesterday at 9:19 PM
by EpicBird08
Source: USAMO 2022/4, JMO 2022/5
Find all pairs of primes
for which
and
are both perfect squares.



133 replies
MAA finally wrote sum good number theory
IAmTheHazard 96
N
Yesterday at 4:54 PM
by megahertz13
Source: 2021 AIME I P14
For any positive integer
denotes the sum of the positive integer divisors of
Let
be the least positive integer such that
is divisible by
for all positive integers
Find the sum of the prime factors in the prime factorization of








96 replies
