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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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Greece JBMO TST
ultralako   26
N 28 minutes ago by Adywastaken
Source: Greece JBMO TST Problem 4
Find all positive integers $x,y,z$ with $z$ odd, which satisfy the equation:

$$2018^x=100^y + 1918^z$$
26 replies
ultralako
Apr 22, 2018
Adywastaken
28 minutes ago
J
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An innocent-looking inequality
Bryan0224   1
N 30 minutes ago by Quantum-Phantom
Source: Idk
If $\{a_i\}_{1\le i\le n }$ and $\{b_i\}_{1\le i\le n}$ are two sequences between $1$ and $2$ and they satisfy $\sum_{i=1}^n a_i^2=\sum_{i=1}^n b_i^2$, prove that $\sum_{i=1}^n\frac{a_i^3}{b_i}\leq 1.7\sum_{i=1}^{n} a_i^2$, and determine when does equality hold
Please answer this @sqing :trampoline:
1 reply
Bryan0224
5 hours ago
Quantum-Phantom
30 minutes ago
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Inspired by Turkey 2025
sqing   0
31 minutes ago
Source: Own
Let $ a, b, c >0, a^2 + \frac{b}{a} = 8 $ and $ ab + c^2 \leq 18 .$ Prove that $$ 3a + b + c\leq 9\sqrt{3}$$

0 replies
sqing
31 minutes ago
0 replies
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ISI UGB 2025 P7
SomeonecoolLovesMaths   8
N 44 minutes ago by Mathworld314
Source: ISI UGB 2025 P7
Consider a ball that moves inside an acute-angled triangle along a straight line, unit it hits the boundary, which is when it changes direction according to the mirror law, just like a ray of light (angle of incidence = angle of reflection). Prove that there exists a triangular periodic path for the ball, as pictured below.

IMAGE
8 replies
1 viewing
SomeonecoolLovesMaths
Yesterday at 11:28 AM
Mathworld314
44 minutes ago
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sqrt(n) or n+p (Generalized 2017 IMO/1)
vincentwant   1
N May 8, 2025 by vincentwant
Let $p$ be an odd prime. Define $f(n)$ over the positive integers as follows:
$$f(n)=\begin{cases} \sqrt{n}&\text{ if n is a perfect square} \\ n+p&\text{ otherwise} \end{cases}$$
Let $p$ be chosen such that there exists an ordered pair of positive integers $(n,k)$ where $n>1,p\nmid n$ such that $f^k(n)=n$. Prove that there exists at least three integers $i$ such that $1\leq i\leq k$ and $f^i(n)$ is a perfect square.
1 reply
vincentwant
Apr 30, 2025
vincentwant
May 8, 2025
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sqrt(n) or n+p (Generalized 2017 IMO/1)
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vincentwant
1411 posts
vincentwant
#1 h  Apr 30, 2025, 3:51 PM
Y by
Let $p$ be an odd prime. Define $f(n)$ over the positive integers as follows:
$$f(n)=\begin{cases} \sqrt{n}&\text{ if n is a perfect square} \\ n+p&\text{ otherwise} \end{cases}$$
Let $p$ be chosen such that there exists an ordered pair of positive integers $(n,k)$ where $n>1,p\nmid n$ such that $f^k(n)=n$. Prove that there exists at least three integers $i$ such that $1\leq i\leq k$ and $f^i(n)$ is a perfect square.
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vincentwant
1411 posts
vincentwant
#2 h  May 8, 2025, 2:32 AM
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bumping this
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