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.
3 M G
BBookmark  VNew Topic kLocked
Contests & Programs AMC and other contests, summer programs, etc.
AMC and other contests, summer programs, etc.
3 M G
BBookmark  VNew Topic kLocked
G
Topic
First Poster
Last Poster
Two Sequences
worthawholebean   11
N an hour ago by P162008
Source: AIME 2008II Problem 6
The sequence $ \{a_n\}$ is defined by
\[ a_0 = 1,a_1 = 1, \text{ and } a_n = a_{n - 1} + \frac {a_{n - 1}^2}{a_{n - 2}}\text{ for }n\ge2.
\]The sequence $ \{b_n\}$ is defined by
\[ b_0 = 1,b_1 = 3, \text{ and } b_n = b_{n - 1} + \frac {b_{n - 1}^2}{b_{n - 2}}\text{ for }n\ge2.
\]Find $ \frac {b_{32}}{a_{32}}$.
11 replies
worthawholebean
Apr 3, 2008
P162008
an hour ago
OTIS or MathWOOT 2
math_on_top   12
N Today at 1:38 AM 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
Today at 1:38 AM
looks like roots of unity filter!
math31415926535   37
N Yesterday at 9:06 PM by xHypotenuse
Source: 2022 AIME II Problem 13
There is a polynomial $P(x)$ with integer coefficients such that $$P(x)=\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)}$$holds for every $0<x<1.$ Find the coefficient of $x^{2022}$ in $P(x)$
37 replies
math31415926535
Feb 17, 2022
xHypotenuse
Yesterday at 9:06 PM
OMMC TEAM
isache   20
N Yesterday at 8:32 PM by steve4916
Hi everyone, im looking for an OMMC team. I have currently solved problems 1-16 with the exception of 13. Also, I would prefer if your team currently has 2 or 3 members. My stats:

133.5 on 10B this year
9 on aime this year, 8 the previous
24 on AMC 8
Orange County (CA) Mathcounts Champion in 8th and runner up in 7th
USCMC 4th place written 2nd place countdown (lost to tiger zhang)
UCSD HMM 5th place
SMT 15th place algebra round
nita main
3x AIME qual
3x AMC 10hr
20 replies
isache
May 19, 2025
steve4916
Yesterday at 8:32 PM
[$10K+ IN PRIZES] Poolesville Math Tournament (PVMT) 2025
qwerty123456asdfgzxcvb   16
N Yesterday at 7:46 PM by Inaaya
Hi everyone!

After the resounding success of the first three years of PVMT, the Poolesville High School Math Team is excited to announce the fourth annual Poolesville High School Math Tournament (PVMT)! The PVMT team includes a MOPper and multiple USA(J)MO and AIME qualifiers!

PVMT is open to all 6th-9th graders in the country (including rising 10th graders). Students will compete in teams of up to 4 people, and each participant will take three subject tests as well as the team round. The contest is completely free, and will be held virtually on June 7, 2025, from 10:00 AM to 4:00 PM (EST).

Additionally, thanks to our sponsors, we will be awarding approximately $10K+ worth of prizes (including gift cards, Citadel merch, AoPS coupons, Wolfram licenses) to top teams and individuals. More details regarding the actual prizes will be released as we get closer to the competition date.

Further, newly for this year we might run some interesting mini-events, which we will announce closer to the competition date, such as potentially a puzzle hunt and integration bee!

If you would like to register for the competition, the registration form can be found at https://pvmt.org/register.html or https://tinyurl.com/PVMT25.

Additionally, more information about PVMT can be found at https://pvmt.org

If you have any questions not answered in the below FAQ, feel free to ask in this thread or email us at falconsdomath@gmail.com!

We look forward to your participation!

FAQ
16 replies
qwerty123456asdfgzxcvb
Apr 5, 2025
Inaaya
Yesterday at 7:46 PM
Coordbashing = 0?
UberPiggy   14
N Yesterday at 6:38 PM by Math4Life2020
Hi,

I just received my USAJMO score distribution: 000 701 (very cursed I know)

The thing is, I solved #5 (Geometry) by using Cartesian coordinates and tried to show a lot of detail in my calculations. I don't think I mislabeled the pages or anything either. I don't have the scans, but does anyone know why this might be the case? Thank you!
14 replies
UberPiggy
Apr 23, 2025
Math4Life2020
Yesterday at 6:38 PM
MAA messed up the order(n)
skipiano   200
N Yesterday at 6:23 PM by Rayvhs
Source: 2017 USAJMO #1/USAMO #1
Prove that there are infinitely many distinct pairs $(a, b)$ of relatively prime integers $a>1$ and $b>1$ such that $a^b+b^a$ is divisible by $a+b$.
200 replies
skipiano
Apr 19, 2017
Rayvhs
Yesterday at 6:23 PM
Units Digit of Monomial/Exponent
worthawholebean   21
N Yesterday at 5:50 PM by P162008
Source: AMC 12 2008A Problem 15
Let $ k=2008^2+2^{2008}$. What is the units digit of $ k^2+2^k$?

$ \textbf{(A)}\ 0 \qquad
\textbf{(B)}\ 2 \qquad
\textbf{(C)}\ 4 \qquad
\textbf{(D)}\ 6 \qquad
\textbf{(E)}\ 8$
21 replies
worthawholebean
Feb 17, 2008
P162008
Yesterday at 5:50 PM
Join My OMMC Team?
RupertStream   0
Yesterday at 5:34 PM
Hey would anyone like to join my team The MVPs for the OMMC? It is happening right now and I realize that, I have no chance of finishing it within the 8 day time limit. It is free to compete and you can win money just say you want to join and I can add you and send the test to your gmail.
0 replies
RupertStream
Yesterday at 5:34 PM
0 replies
USAJMO problem 3: Inequality
BOGTRO   105
N Yesterday at 5:17 PM by Adywastaken
Let $a,b,c$ be positive real numbers. Prove that $\frac{a^3+3b^3}{5a+b}+\frac{b^3+3c^3}{5b+c}+\frac{c^3+3a^3}{5c+a} \geq \frac{2}{3}(a^2+b^2+c^2)$.
105 replies
BOGTRO
Apr 24, 2012
Adywastaken
Yesterday at 5:17 PM
9 USAMO/JMO
BAM10   16
N Yesterday at 5:11 PM by Schintalpati
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
16 replies
BAM10
Monday at 11:31 PM
Schintalpati
Yesterday at 5:11 PM
a