what is a moh

by Soupboy0, Mar 23, 2025, 6:49 PM

can someone please tell me what a moh is

USAMO Grading

by AdityaDwivedi, Mar 23, 2025, 4:21 PM

Hello,

I was wondering how USAMO grading works. For one of my solutions, I kinda generalized a part of my solution cause I assumed that the reader would be able to follow but idk if it’ll drop my score from a 7 to a 5 or 6. So how much detail to I rlly need to include to get full points?

mohs of each oly

by cowstalker, Mar 23, 2025, 1:20 AM

what are the general concencus for the mohs of each of the problems on usajmo and usamo

USAMO

USA(J)MO

USAJMO

Red Mop Chances

by imagien_bad, Mar 22, 2025, 8:27 PM

What are my chances of making red mop with a 35 on jmo?

funny title placeholder

by pikapika007, Mar 21, 2025, 12:10 PM

Let $S$ be a set of integers with the following properties:

$\{ 1, 2, \dots, 2025 \} \subseteq S$ .
If $a, b \in S$ and $\gcd(a, b) = 1$ , then $ab \in S$ .
If for some $s \in S$ , $s + 1$ is composite, then all positive divisors of $s + 1$ are in $S$ .

Prove that $S$ contains all positive integers.

This post has been edited 1 time. Last edited by pikapika007, Mar 21, 2025, 12:12 PM
Reason: wrong year

AMC

USA(J)MO

USAJMO

Scary Binomial Coefficient Sum

by EpicBird08, Mar 21, 2025, 11:59 AM

Determine, with proof, all positive integers $k$ such that $\frac{1}{n+1} \sum_{i=0}^n \binom{n}{i}^k$ is an integer for every positive integer $n.$

This post has been edited 2 times. Last edited by EpicBird08, Mar 21, 2025, 12:06 PM

AMC

USA(J)MO

USAMO

Prove a polynomial has a nonreal root

by KevinYang2.71, Mar 20, 2025, 12:00 PM

Let $n$ and $k$ be positive integers with $k<n$ . Let $P(x)$ be a polynomial of degree $n$ with real coefficients, nonzero constant term, and no repeated roots. Suppose that for any real numbers $a_0,\,a_1,\,\ldots,\,a_k$ such that the polynomial $a_kx^k+\cdots+a_1x+a_0$ divides $P(x)$ , the product $a_0a_1\cdots a_k$ is zero. Prove that $P(x)$ has a nonreal root.

AMC

USA(J)MO

USAMO

ABMC 2025 IN-PERSON Contest (April 5th)

by ilovepizza2020, Mar 16, 2025, 11:32 PM

The 9th annual Acton-Boxborough Math Competition (ABMC) is quickly approaching! This year's ABMC will be held in-person at RJ Grey Junior High School, Acton, MA, on April 5th, 2025. The competition includes individual rounds and a team round, in which teams of 2-4 students participate. Anyone in grade 8 or below is welcome! You must register to compete. For more information about registration and the tentative schedule, please consult our website: https://abmathcompetitions.org/2025-contest/.

We offer prizes not only to top competitors; several of our sponsor prizes and educational awards are raffled among all in-person participants. Additionally, there are separate prizes for the top-scoring elementary schoolers.

For more information, visit https://abmathcompetitions.org/, especially the 2025 Competition page.
For the mailing list, visit https://abmathcompetitions.org/contact/.

Best,
ABMC Coordinators

Attachments:

ABMC Onsite Flier 2025.pdf (160kb)

ABMC

[TEST RELEASED] Mock Geometry Test for College Competitions

by Bluesoul, Feb 24, 2025, 9:42 AM

Hi AOPSers,

I have finished writing a mock geometry test for fun and practice for the real college competitions like HMMT/PUMaC/CMIMC... There would be 10 questions and you should finish the test in 60 minutes, the test would be close to the actual test (hopefully). You could sign up under this thread, PM me your answers!. The submission would close on March 31st at 11:59PM PST.

I would create a private discussion forum so everyone could discuss after finishing the test. This is the first mock I've written, please sign up and enjoy geometry!!

~Bluesoul

Leaderboard

Attachments:

Mock_Geometry Test Final.pdf (91kb)

This post has been edited 7 times. Last edited by Bluesoul, Yesterday at 9:58 PM

geometry

college competitions

A parabolic triangle-USAJMO Problem 4

by BarbieRocks, Apr 29, 2010, 1:33 PM

A triangle is called a parabolic triangle if its vertices lie on a parabola $y = x^2$ . Prove that for every nonnegative integer $n$ , there is an odd number $m$ and a parabolic triangle with vertices at three distinct points with integer coordinates with area $(2^nm)^2$ .

Submit

!!!!!!!!
by stroller, Mar 10, 2020, 8:15 PM
cooooooool
nice blog
by Navansh, Jun 4, 2019, 7:47 AM
Victor is one of the GOATs.
by awesomemathlete, Oct 2, 2018, 11:48 PM
This blog is truly amazing.
by sunfishho, Feb 20, 2018, 6:32 AM
what a gem.
by vjdjmathaddict, May 10, 2017, 3:26 PM
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by ahaanomegas, Dec 15, 2013, 7:21 PM
yo dawg i heard you imo
by Mewto55555, Aug 1, 2013, 10:25 PM
Good job on 5 problems on USAMO. I know that is a pretty bad score for someone as awesome as you on a normal USAMO, but no one got all 6 this year so it's GREAT!

VICTOR WANG 42 ON IMO 2013 LET'S GO.

See you at MOP this year (probably ).
by yugrey, May 3, 2013, 10:32 PM
you can just write "Solution
" instead of "Click to reveal hidden text
"

by math154, Feb 6, 2013, 6:33 PM
Hello. May I ask a stupid question: how to turn "Hidden Text" into hidden "Solution" tag?
by ysymyth, Feb 1, 2013, 12:59 PM
This is a good blog.I like it.
by Lingqiao, Jul 17, 2012, 4:21 PM
hi.i like the blog.
by Dranzer, Feb 9, 2012, 12:25 PM
sorry, i've decided this blog is just for the random stuff i do. don't take it personally... you can always post things on your own blog
by math154, Nov 23, 2011, 10:26 PM
what i got uncontribbed for posting a nice geo problem?
by yugrey, Nov 23, 2011, 1:32 AM
Can I be a contributor?
by Binomial-theorem, Oct 5, 2011, 12:39 AM
by gauss1181, Mar 8, 2009, 5:09 PM
i hate you
by alsyy, Mar 8, 2009, 4:37 PM
Fine. I don't care.
by math154, Mar 8, 2009, 1:34 AM
Math154: It was West Somethign Middle School from Columbia that got 2nd.
by Mewto55555, Mar 8, 2009, 1:20 AM
Oh dang, I already feel like deleting this blog. Maybe I should not do that for a while, though.
by math154, Mar 6, 2009, 2:50 AM
math154 mew and tinytim tied for first at chapter...
by AIME15, Mar 6, 2009, 1:06 AM
Thanks! Good luck to you too.
by math154, Mar 5, 2009, 1:00 AM
good luck on saturday
by gauss1181, Mar 5, 2009, 12:51 AM
Yeah gauss, our chapter sends the top 50 individuals and the top 10 teams.
by math154, Mar 4, 2009, 10:49 PM
Me wants be contrib.
by AIME15, Mar 4, 2009, 5:07 PM
I'll contrib in the future when I feel like it. I'm not gonna forget you, though, so don't worry.
by math154, Mar 2, 2009, 11:55 PM
third! contrib?
by nikeballa96, Mar 2, 2009, 10:40 PM
2nd Shout!
by gauss1181, Feb 28, 2009, 5:25 PM
1st Shout!
by mathemagician1729, Feb 28, 2009, 4:02 AM