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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.
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[*]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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Prime sums of pairs
Assassino9931   0
a minute ago
Source: Al-Khwarizmi Junior International Olympiad 2025 P5
Sevara writes in red $8$ distinct positive integers and then writes in blue the $28$ sums of each two red numbers. At most how many of the blue numbers can be prime?

Marin Hristov, Bulgaria
0 replies
Assassino9931
a minute ago
0 replies
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help me solve this problem. Thanks
tnhan.129   0
3 minutes ago
Find f:R+ -> R such that:
(x+1/x).f(y) = f(xy) + f(y/x)
0 replies
tnhan.129
3 minutes ago
0 replies
J
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Line passing through orthocenter
pokmui9909   4
N 4 minutes ago by Tkn
Source: KMO 2024 P7
In an acute triangle $ABC$, let a line $\ell$ pass through the orthocenter and not through point $A$. The line $\ell$ intersects line $BC$ at $P(\neq B, C)$. A line passing through $A$ and perpendicular to $\ell$ meets the circumcircle of triangle $ABC$ at $R(\neq A)$. Let the feet of the perpendiculars from $A, B$ to $\ell$ be $A', B'$, respectively. Define line $\ell_1$ as the line passing through $A'$ and perpendicular to $BC$, and line $\ell_2$ as the line passing through $B'$ and perpendicular to $CA$. Prove that if $Q$ is the reflection of the intersection of $\ell_1$ and $\ell_2$ across $\ell$, then $\angle PQR = 90^{\circ}$.
4 replies
1 viewing
pokmui9909
Nov 9, 2024
Tkn
4 minutes ago
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Inequality with number of divisors
MathLuis   12
N 13 minutes ago by Grasshopper-
Source: Iberoamerican MO 2024 Day 1 P1
For each positive integer $n$, let $d(n)$ be the number of positive integer divisors of $n$.
Prove that for all pairs of positive integers $(a,b)$ we have that:
\[ d(a)+d(b) \le d(\gcd(a,b))+d(\text{lcm}(a,b)) \]and determine all pairs of positive integers $(a,b)$ where we have equality case.
12 replies
MathLuis
Sep 21, 2024
Grasshopper-
13 minutes ago
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No more topics!
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Functional equation in R^2
EmilXM   2
N Apr 10, 2025 by jasperE3
Source: Own
Find all functions $f:\mathbb{R}^2 \longrightarrow \mathbb{R}$, such that: \begin{align*} f(f(x,y),y^2) = f(x^2,0) + 2yf(x,y) \end{align*}For all $x,y \in \mathbb{R}$.

@below fixed.
2 replies
EmilXM
Oct 14, 2020
jasperE3
Apr 10, 2025
J
Functional equation in R^2
G H J
Reveal topic tags
algebra
functional equation
function
fe unsolved
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G H BBookmark kLocked kLocked NReply
Source: Own
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EmilXM
378 posts
EmilXM
#1 h  Oct 14, 2020, 12:13 PM
Y by
Find all functions $f:\mathbb{R}^2 \longrightarrow \mathbb{R}$, such that: \begin{align*} f(f(x,y),y^2) = f(x^2,0) + 2yf(x,y) \end{align*}For all $x,y \in \mathbb{R}$.

@below fixed.
This post has been edited 1 time. Last edited by EmilXM, Oct 14, 2020, 12:31 PM
Reason: Typo
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pco
23511 posts
pco
#2 h  Oct 14, 2020, 12:28 PM
Y by
EmilXM wrote:
Find all functions $f:\mathbb{R}^2 \longrightarrow \mathbb{R}^2$, such that: \begin{align*} f(f(x,y),y^2) = f(x^2,0) + 2yf(x,y) \end{align*}For all $x,y \in \mathbb{R}$.
No such function : since $f(x,y)\in\mathbb R^2$, then $f(f(x,y),y^2)$ is undefined (first argument is not a real, but a pair)
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jasperE3
11317 posts
jasperE3
#3 h  Apr 10, 2025, 10:31 PM
Y by
bump, unsolved$~~~~~~$
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