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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)!

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[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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Bulgaria National Olympiad 1996
Jjesus   7
N 2 minutes ago by reni_wee
Find all prime numbers $p,q$ for which $pq$ divides $(5^p-2^p)(5^q-2^q)$.
7 replies
Jjesus
Jun 10, 2020
reni_wee
2 minutes ago
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Can't be power of 2
shobber   31
N 2 minutes ago by LeYohan
Source: APMO 1998
Show that for any positive integers $a$ and $b$, $(36a+b)(a+36b)$ cannot be a power of $2$.
31 replies
shobber
Mar 17, 2006
LeYohan
2 minutes ago
J
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Brilliant Problem
M11100111001Y1R   4
N 13 minutes ago by IAmTheHazard
Source: Iran TST 2025 Test 3 Problem 3
Find all sequences \( (a_n) \) of natural numbers such that for every pair of natural numbers \( r \) and \( s \), the following inequality holds:
\[ \frac{1}{2} < \frac{\gcd(a_r, a_s)}{\gcd(r, s)} < 2 \]
4 replies
M11100111001Y1R
Yesterday at 7:28 AM
IAmTheHazard
13 minutes ago
J
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Own made functional equation
Primeniyazidayi   1
N 27 minutes ago by Primeniyazidayi
Source: own(probably)
Find all functions $f:R \rightarrow R$ such that $xf(x^2+2f(y)-yf(x))=f(x)^3-f(y)(f(x^2)-2f(x))$ for all $x,y \in \mathbb{R}$
1 reply
Primeniyazidayi
May 26, 2025
Primeniyazidayi
27 minutes ago
J
No more topics!
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J
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The smallest of sum of elements
hlminh   1
N Apr 23, 2025 by nguyenhuybao_06
Let $S=\{1,2,...,2014\}$ and $X\subset S$ such that for all $a,b\in X,$ if $a+b\leq 2014$ then $a+b\in X.$ Find the smallest of sum of all elements of $X.$
1 reply
hlminh
Apr 23, 2025
nguyenhuybao_06
Apr 23, 2025
J
The smallest of sum of elements
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Reveal topic tags
combinatorics
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hlminh
241 posts
hlminh
#1 h  Apr 23, 2025, 6:33 PM
Y by
Let $S=\{1,2,...,2014\}$ and $X\subset S$ such that for all $a,b\in X,$ if $a+b\leq 2014$ then $a+b\in X.$ Find the smallest of sum of all elements of $X.$
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nguyenhuybao_06
39 posts
nguyenhuybao_06
#2 h  Apr 23, 2025, 6:44 PM
Y by
This problem is tricky lol.
If $a+b\in X, a+b\le 2024,$ then $a+b \in X.$ Note that since $X$ is a finite set, there exists $x,y\in X$ such that $x+y\ge 2025.$ So that the smallest of sum of all elements of $X$ is $2025.$
For the construction, $X=\lbrace1007,1008\rbrace.$
This post has been edited 1 time. Last edited by nguyenhuybao_06, Apr 23, 2025, 6:44 PM
Reason: typo
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