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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
Thursday at 11:16 PM
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.

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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
Thursday at 11:16 PM
0 replies
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all functions satisfying f(x+yf(x))+y = xy + f(x+y)
falantrng   33
N 2 minutes ago by ioannism45
Source: Balkan MO 2025 P3
Find all functions $f\colon \mathbb{R} \rightarrow \mathbb{R}$ such that for all $x,y \in \mathbb{R}$,
\[f(x+yf(x))+y = xy + f(x+y).\]
Proposed by Giannis Galamatis, Greece
33 replies
falantrng
Apr 27, 2025
ioannism45
2 minutes ago
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Solution needed ASAP
UglyScientist   8
N 7 minutes ago by deltapc
$ABC$ is acute triangle. $H$ is orthocenter, $M$ is the midpoint of $BC$, $L$ is the midpoint of smaller arc $BC$. Point $K$ is on $AH$ such that, $MK$ is perpendicular to $AL$. Prove that: $HMLK$ is paralelogram(Synthetic sol needed).
8 replies
UglyScientist
4 hours ago
deltapc
7 minutes ago
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BMO 2024 SL C1
GreekIdiot   11
N 26 minutes ago by cursed_tangent1434
Let $n$, $k$ be positive integers. Julia and Florian play a game on a $2n \times 2n$ board. Julia
has secretly tiled the entire board with invisible dominos. Florian now chooses $k$ cells.
All dominos covering at least one of these cells then turn visible. Determine the minimal
value of $k$ such that Florian has a strategy to always deduce the entire tiling.
11 replies
GreekIdiot
Apr 27, 2025
cursed_tangent1434
26 minutes ago
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Cyclic quadrilateral and a tangent
a_507_bc   6
N 33 minutes ago by User141208
Source: IMOC 2023 G6
Triangle $ABC$ has circumcenter $O$. $D$ is the foot from $A$ to $BC$, and $P$ is apoint on $AD$. The feet from $P$ to $CA, AB$ are $E, F$, respectively, and the foot from $D$ to $EF$ is $T$. $AO$ meets $(ABC)$ again at $A'$. $A'D$ meets $(ABC)$ again at $R$. If $Q$ is a point on $AO$ satisfying $\angle ABP = \angle QBC$, prove that $D, P, T, R$ lie on acircle and $DQ$ is tangent to it.
6 replies
1 viewing
a_507_bc
Sep 9, 2023
User141208
33 minutes ago
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No more topics!
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hard problem
Rename   2
N Apr 28, 2025 by Rename
Determine the largest constant $K\geq 0$ so that:
$$\frac{a^a(b^2+c^2)}{(a^a-1)^2}+\frac{b^b(c^2+a^2)}{(b^b-1)^2}+\frac{c^c(a^2+b^2)}{(c^c-1)^2}\geq K\left (\frac{a+b+c}{abc-1}\right)^2$$with all real numbers $a; b; c$ satisfies $ab+bc+ca=abc$

P/s: Do you know which exam question this problem is actually in, at first I remembered but now I forgot
2 replies
Rename
Apr 27, 2025
Rename
Apr 28, 2025
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hard problem
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inequalities
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Rename
327 posts
Rename
#1 h  Apr 27, 2025, 3:24 PM
Y by
Determine the largest constant $K\geq 0$ so that:
$$\frac{a^a(b^2+c^2)}{(a^a-1)^2}+\frac{b^b(c^2+a^2)}{(b^b-1)^2}+\frac{c^c(a^2+b^2)}{(c^c-1)^2}\geq K\left (\frac{a+b+c}{abc-1}\right)^2$$with all real numbers $a; b; c$ satisfies $ab+bc+ca=abc$

P/s: Do you know which exam question this problem is actually in, at first I remembered but now I forgot
This post has been edited 1 time. Last edited by Rename, Apr 27, 2025, 3:24 PM
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GeoMorocco
38 posts
GeoMorocco
#2 h  Apr 27, 2025, 9:56 PM
Y by
Rename wrote:
Determine the largest constant $K\geq 0$ so that:
$$\frac{a^a(b^2+c^2)}{(a^a-1)^2}+\frac{b^b(c^2+a^2)}{(b^b-1)^2}+\frac{c^c(a^2+b^2)}{(c^c-1)^2}\geq K\left (\frac{a+b+c}{abc-1}\right)^2$$with all real numbers $a; b; c$ satisfies $ab+bc+ca=abc$

P/s: Do you know which exam question this problem is actually in, at first I remembered but now I forgot

I believe $K = 18$ at $a=b=c=3$.
This post has been edited 1 time. Last edited by GeoMorocco, Apr 28, 2025, 8:36 AM
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Rename
327 posts
Rename
#3 h  Apr 28, 2025, 8:31 AM
Y by
Yes you right, do you know which exam question this problem is actually in
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