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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]
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0 replies
jlacosta
May 1, 2025
0 replies
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Goals for 2025-2026
Airbus320-214   157
N 12 minutes ago by isache
Please write down your goal/goals for competitions here for 2025-2026.
157 replies
Airbus320-214
May 11, 2025
isache
12 minutes ago
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[TEST RELEASED] OMMC Year 5
DottedCaculator   97
N 2 hours ago by sagayao
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/
Our Discord (6000+ members): https://tinyurl.com/joinommc

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]
97 replies
DottedCaculator
Apr 26, 2025
sagayao
2 hours ago
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Essentially, how to get good at olympiad math?
gulab_jamun   10
N 3 hours ago by gulab_jamun
Ok, so I'm posting this as an anynonymous user cuz I don't want to get flamed by anyone I know for my goals but I really do want to improve on my math skill.

Basically, I'm alright at computational math (10 AIME, dhr stanford math meet twice) and I hope I can get good enough at olympiad math over the summer to make MOP next year (I will be entering 10th as after next year, it becomes much harder :( )) Essentially, I just want to get good at olympiad math. If someone could, please tell me how to study, like what books (currently thinking of doing EGMO) but I don't know how to get better at the other topics. Also, how would I prepare? Like would I study both proof geometry and proof number theory concurrently or just study each topic one by one?? Would I do mock jmo/amo or js prioritize olympiad problems in each topic. I have the whole summer ahead of me, and intend to dedicate it to olympiad math, so any advice would be really appreciated. Thank you!
10 replies
gulab_jamun
May 18, 2025
gulab_jamun
3 hours ago
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OTIS or MathWOOT 2
math_on_top   12
N 4 hours ago by N3bula
Hey AoPS community I took MathWOOT 1 this year and scored an 8 on AIME (last year I got a 6). My goal is to make it to MOP next year through USAMO. It's gonna be a lot of work, but do you think that I should do MathWOOT 2 or OTIS? Personally, I felt that MathWOOT 1 taught me a lot but was more focused on computational - not sure how to split computation vs olympiad prep. So, for those who can address this question:

(1) How much compuational vs olympiad
(2) OTIS or MathWOOT 2 and why
12 replies
math_on_top
May 18, 2025
N3bula
4 hours ago
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f(2x+y)=f(x+2y)
jasperE3   3
N 5 hours ago by MathIQ.
Find all functions $f:\mathbb R^+\to\mathbb R^+$ such that:
$$f(2x+y)=f(x+2y)$$for all $x,y>0$.
3 replies
jasperE3
Yesterday at 8:58 PM
MathIQ.
5 hours ago
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Inequalities
sqing   13
N Yesterday at 8:41 PM by ytChen
Let $ a,b>0 $ . Prove that
$$ \frac{a}{a^2+a +2b+1}+ \frac{b}{b^2+2a +b+1} \leq \frac{2}{5} $$$$ \frac{a}{a^2+2a +b+1}+ \frac{b}{b^2+a +2b+1} \leq \frac{2}{5} $$
13 replies
sqing
May 13, 2025
ytChen
Yesterday at 8:41 PM
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System of Equations
P162008   1
N Yesterday at 8:31 PM by alexheinis
If $a,b$ and $c$ are real numbers such that

$(a + b)(b + c) = -1$

$(a - b)^2 + (a^2 - b^2)^2 = 85$

$(b - c)^2 + (b^2 - c^2)^2 = 75$

Compute $(a - c)^2 + (a^2 - c^2)^2.$
1 reply
P162008
Monday at 10:48 AM
alexheinis
Yesterday at 8:31 PM
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Might be the first equation marathon
steven_zhang123   35
N Yesterday at 7:09 PM by lightsbug
As far as I know, it seems that no one on HSM has organized an equation marathon before. Click to reveal hidden textSo why not give it a try? Click to reveal hidden text Let's start one!
Some basic rules need to be clarified:
$\cdot$ If a problem has not been solved within $5$ days, then others are eligible to post a new probkem.
$\cdot$ Not only simple one-variable equations, but also systems of equations are allowed.
$\cdot$ The difficulty of these equations should be no less than that of typical quadratic one-variable equations. If the problem involves higher degrees or more variables, please ensure that the problem is solvable (i.e., has a definite solution, rather than an approximate one).
$\cdot$ Please indicate the domain of the solution to the equation (e.g., solve in $\mathbb{R}$, solve in $\mathbb{C}$).
Here's an simple yet fun problem, hope you enjoy it :P :
P1
35 replies
steven_zhang123
Jan 20, 2025
lightsbug
Yesterday at 7:09 PM
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Maximum number of empty squares
Ecrin_eren   0
Yesterday at 6:35 PM


There are 16 kangaroos on a giant 4×4 chessboard, with exactly one kangaroo on each square. In each round, every kangaroo jumps to a neighboring square (up, down, left, or right — but not diagonally). All kangaroos stay on the board. More than one kangaroo can occupy the same square. What is the maximum number of empty squares that can exist after 100 rounds?



0 replies
Ecrin_eren
Yesterday at 6:35 PM
0 replies
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THREE People Meet at the SAME. TIME.
LilKirb   7
N Yesterday at 5:33 PM by hellohi321
Three people arrive at the same place independently, at a random between $8:00$ and $9:00.$ If each person remains there for $20$ minutes, what's the probability that all three people meet each other?

I'm already familiar with the variant where there are only two people, where you Click to reveal hidden text It was an AIME problem from the 90s I believe. However, I don't know how one could visualize this in a Click to reveal hidden text Help on what to do?
7 replies
LilKirb
Monday at 1:06 PM
hellohi321
Yesterday at 5:33 PM
J
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Quite straightforward
steven_zhang123   1
N Yesterday at 3:16 PM by Mathzeus1024
Given that the sequence $\left \{ a_{n} \right \} $ is an arithmetic sequence, $a_{1}=1$, $a_{2}+a_{3}+\dots+a_{10}=144$. Let the general term $b_{n}$ of the sequence $\left \{ b_{n} \right \}$ be $\log_{a}{(1+\frac{1}{a_{n}} )} ( a > 0 \text{and} a \ne 1)$, and let $S_{n}$ be the sum of the $n$ terms of the sequence $\left \{ b_{n} \right \}$. Compare the size of $S_{n}$ with $\frac{1}{3} \log_{a}{(1+\frac{1}{a_{n}} )} $.
1 reply
steven_zhang123
Jan 11, 2025
Mathzeus1024
Yesterday at 3:16 PM
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Inequalities
sqing   0
Yesterday at 2:23 PM
Let $ a,b,c>0. $ Prove that$$a^2+b^2+c^2+abc-k(a+b+c)\geq 3k+2-2(k+1)\sqrt{k+1}$$Where $7\geq k \in N^+.$
$$a^2+b^2+c^2+abc-3(a+b+c)\geq-5$$
0 replies
sqing
Yesterday at 2:23 PM
0 replies
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Function and Quadratic equations help help help
Ocean_MathGod   1
N Yesterday at 11:26 AM by Mathzeus1024
Consider this parabola: y = x^2 + (2m + 1)x + m(m - 3) where m is constant and -1 ≤ m ≤ 4. A(-m-1, y1), B(m/2, y2), C(-m, y3) are three different points on the parabola. Now rotate the axis of symmetry of the parabola 90 degrees counterclockwise around the origin O to obtain line a. Draw a line from the vertex P of the parabola perpendicular to line a, meeting at point H.

1) express the vertex of the quadratic equation using an expression with m.
2) If, regardless of the value of m, the parabola and the line y=x−km (where k is a constant) have exactly one point of intersection, find the value of k.

3) (where I'm struggling the most) When 1 < PH ≤ 6, compare the values of y1, y2, and y3.
1 reply
Ocean_MathGod
Aug 26, 2024
Mathzeus1024
Yesterday at 11:26 AM
J
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System of Equations
P162008   1
N Yesterday at 10:30 AM by alexheinis
If $a,b$ and $c$ are complex numbers such that

$\frac{ab}{b + c} + \frac{bc}{c + a} + \frac{ca}{a + b} = -9$

$\frac{ab}{c + a} + \frac{bc}{a + b} + \frac{ca}{b + c} = 10$

Compute $\frac{a}{c + a} + \frac{b}{a + b} + \frac{c}{b + c}.$
1 reply
P162008
Monday at 10:34 AM
alexheinis
Yesterday at 10:30 AM
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J
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Modular Arithmetic Handout
MathCosine   18
N Apr 11, 2025 by nsking_1209
Hi everyone,

I recently created a handout on modular arithmetic for a local math club. I thought it would help quite a lot with understanding basic properties, as modular arithmetic is a very popular intermediate step in number theory problems, so I decided to leave it here as a resource for anyone who needs it. Feel free to share it around, and hope it helps!

Sincerely,
MathCosine
18 replies
MathCosine
Apr 7, 2025
nsking_1209
Apr 11, 2025
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Modular Arithmetic Handout
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Reveal topic tags
number theory
modular arithmetic
Handout
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MathCosine
169 posts
MathCosine
#1 h  Apr 7, 2025, 8:52 PM • 3 Y
Y by Awesome_Twin1, Pengu14, Sedro
Hi everyone,

I recently created a handout on modular arithmetic for a local math club. I thought it would help quite a lot with understanding basic properties, as modular arithmetic is a very popular intermediate step in number theory problems, so I decided to leave it here as a resource for anyone who needs it. Feel free to share it around, and hope it helps!

Sincerely,
MathCosine
Attachments:
Modular_Arithmetic_Intro_v1.pdf (137kb)
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jb2015007
1968 posts
jb2015007
#2 h  Apr 7, 2025, 8:58 PM
Y by
yeesssss ty i need this
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franklin2013
300 posts
franklin2013
#3 h  Apr 7, 2025, 9:02 PM
Y by
same for me tysm!
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Jaxman8
122 posts
Jaxman8
#4 h  Apr 7, 2025, 9:15 PM
Y by
Is there an intermediate
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jb2015007
1968 posts
jb2015007
#5 h  Apr 7, 2025, 9:57 PM
Y by
pls make more! People like me need them!

also another suggestion is make them a tad longer other than that though, its amazing!
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sadas123
1318 posts
sadas123
#6 h  Apr 7, 2025, 9:58 PM
Y by
Jaxman8 wrote:
Is there an intermediate

Eulers tolient helps to find the number of positive integers that are relatively prime to x and below right?
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sadas123
1318 posts
sadas123
#7 h  Apr 7, 2025, 9:59 PM
Y by
sadas123 wrote:
Jaxman8 wrote:
Is there an intermediate

Eulers tolient helps to find the number of positive integers that are relatively prime to x and below right?

I am a bit rusty to number Theory srry
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mathprodigy2011
342 posts
mathprodigy2011
#8 h  Apr 7, 2025, 10:10 PM
Y by
sadas123 wrote:
Jaxman8 wrote:
Is there an intermediate

Eulers tolient helps to find the number of positive integers that are relatively prime to x and below right?

Number of positive integers less than x which are relatively prime to x is known as eulers totient function or phi(x)
Z K Y
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Pengu14
634 posts
Pengu14
#9 h  Apr 7, 2025, 10:12 PM
Y by
mathprodigy2011 wrote:
sadas123 wrote:
Jaxman8 wrote:
Is there an intermediate

Eulers tolient helps to find the number of positive integers that are relatively prime to x and below right?

Number of positive integers less than x which are relatively prime to x is known as eulers totient function or phi(x)

ADMITS
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greenturtle3141
3560 posts
greenturtle3141
#10 h  Apr 7, 2025, 10:47 PM • 2 Y
Y by scannose, Sedro
Quote:
$$9^{1012} \equiv (-1)^{1012}$$
This is not at all obvious based on what you've written thus far! This trick is too important to simply gloss over.
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lord_of_the_rook
170 posts
lord_of_the_rook
#11 h  Apr 7, 2025, 11:19 PM
Y by
One small nitpick: You say that $a | b$ if there exists $c$ such that $\frac b a = c$. However, we say that $0 | 0$, so I think a better definition would be that there exists some $c$ such that $b = ac$.
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fake123
93 posts
fake123
#12 h  Apr 7, 2025, 11:59 PM
Y by
greenturtle3141 wrote:
Quote:
$$9^{1012} \equiv (-1)^{1012}$$
This is not at all obvious based on what you've written thus far! This trick is too important to simply gloss over.

how? it's just the units digit
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MathCosine
169 posts
MathCosine
#13 h  Apr 8, 2025, 12:18 AM • 1 Y
Y by lord_of_the_rook
lord_of_the_rook wrote:
One small nitpick: You say that $a | b$ if there exists $c$ such that $\frac b a = c$. However, we say that $0 | 0$, so I think a better definition would be that there exists some $c$ such that $b = ac$.

Thanks, I’ll update it soon.
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MathCosine
169 posts
MathCosine
#14 h  Apr 8, 2025, 12:18 AM
Y by
Jaxman8 wrote:
Is there an intermediate

maybe I could… if this is really good, I could try to make another intermediate one for topics like quadratic reciprocity…
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Jaxman8
122 posts
Jaxman8
#15 h  Apr 8, 2025, 12:25 AM
Y by
Yes, this was a really good intro hand out. Thank you!
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idk12345678
394 posts
idk12345678
#16 h  Apr 8, 2025, 2:37 PM • 1 Y
Y by franklin2013
MathCosine wrote:
Jaxman8 wrote:
Is there an intermediate

maybe I could… if this is really good, I could try to make another intermediate one for topics like quadratic reciprocity…

that would be really helpful
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MathCosine
169 posts
MathCosine
#17 h  Apr 10, 2025, 3:18 AM
Y by
Jaxman8 wrote:
Yes, this was a really good intro hand out. Thank you!

Glad you enjoyed it! I'll get to an intermediate one soon.
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N3bula
286 posts
N3bula
#18 h  Apr 11, 2025, 1:01 AM
Y by
MathCosine wrote:
Jaxman8 wrote:
Is there an intermediate

maybe I could… if this is really good, I could try to make another intermediate one for topics like quadratic reciprocity…

wtf is quadratic reciprocity is intermediate wtf is advanced nt just straight up analytic or algebraic nt like bro if ur pulling out cherbatov density in an exam ur trolling
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nsking_1209
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nsking_1209
#19 h  Apr 11, 2025, 4:16 AM
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binomial theorem and wilson's theorem can be used for mods as well
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