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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.

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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 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
J
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Hard Functional Equation in the Complex Numbers
yaybanana   2
N 20 minutes ago by MathIQ.
Source: Own
Find all functions $f:\mathbb {C}\rightarrow \mathbb {C}$, s.t :

$f(xf(y)) + f(x^2+y) = f(x+y)x + f(f(y))$

for all $x,y \in \mathbb{C}$
2 replies
yaybanana
Apr 9, 2025
MathIQ.
20 minutes ago
J
H
xf(x + xy) = xf(x) + f(x^2)f(y)
orl   15
N 28 minutes ago by MathIQ.
Source: MEMO 2008, Team, Problem 5
Determine all functions $ f: \mathbb{R} \mapsto \mathbb{R}$ such that
\[ x f(x + xy) = x f(x) + f \left( x^2 \right) f(y) \quad \forall x,y \in \mathbb{R}.\]
15 replies
orl
Sep 10, 2008
MathIQ.
28 minutes ago
J
H
points on sides of a triangle, intersections, extensions, ratio of areas wanted
parmenides51   2
N an hour ago by MathIQ.
Source: Mexican Mathematical Olympiad 1997 OMM P5
Let $P,Q,R$ be points on the sides $BC,CA,AB$ respectively of a triangle $ABC$. Suppose that $BQ$ and $CR$ meet at $A', AP$ and $CR$ meet at $B'$, and $AP$ and $BQ$ meet at $C'$, such that $AB' = B'C', BC' =C'A'$, and $CA'= A'B'$. Compute the ratio of the area of $\triangle PQR$ to the area of $\triangle ABC$.
2 replies
parmenides51
Jul 28, 2018
MathIQ.
an hour ago
J
H
integer functional equation
ABCDE   156
N an hour ago by MathIQ.
Source: 2015 IMO Shortlist A2
Determine all functions $f:\mathbb{Z}\rightarrow\mathbb{Z}$ with the property that \[f(x-f(y))=f(f(x))-f(y)-1\]holds for all $x,y\in\mathbb{Z}$.
156 replies
ABCDE
Jul 7, 2016
MathIQ.
an hour ago
J
No more topics!
H
J
H
1 line solution to Inequality
ItzsleepyXD   2
N Apr 30, 2025 by Vivaandax
Source: Own , Mock Thailand Mathematic Olympiad P8
Let $x_1,x_2,\dots,x_n$ be positive real number such that $x_1^2+x_2^2+\cdots+x_n^2=2$ Prove that
$$\sum_{i=1}^{n}\frac{1}{x_i^3(x_{i-1}+x_{i+1})}\geqslant \left(\sum_{i=1}^{n}\frac{x_i}{x_{i-1}+x_{i+1}}\right)^3$$such that $x_{n+1}=x_1$ and $x_0=x_n$
2 replies
ItzsleepyXD
Apr 30, 2025
Vivaandax
Apr 30, 2025
J
1 line solution to Inequality
G H J
Reveal topic tags
inequalities
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G H BBookmark kLocked kLocked NReply
Source: Own , Mock Thailand Mathematic Olympiad P8
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ItzsleepyXD
147 posts
ItzsleepyXD
#1 h  Apr 30, 2025, 9:27 AM
Y by
Let $x_1,x_2,\dots,x_n$ be positive real number such that $x_1^2+x_2^2+\cdots+x_n^2=2$ Prove that
$$\sum_{i=1}^{n}\frac{1}{x_i^3(x_{i-1}+x_{i+1})}\geqslant \left(\sum_{i=1}^{n}\frac{x_i}{x_{i-1}+x_{i+1}}\right)^3$$such that $x_{n+1}=x_1$ and $x_0=x_n$
This post has been edited 1 time. Last edited by ItzsleepyXD, May 1, 2025, 1:33 AM
Reason: Positive integer to positive real
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mihaig
7367 posts
mihaig
#2 h  Apr 30, 2025, 1:56 PM
Y by
Difficult, of course. Who is the author?
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Vivaandax
87 posts
Vivaandax
#3 h  Apr 30, 2025, 7:51 PM
Y by
If all the x_i are positive real integers, then x_i can only equal one right???
Did you mean to write positive reals instead of positive integers?
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ItzsleepyXD
147 posts
ItzsleepyXD
#4 h  May 1, 2025, 1:34 AM
Y by
Vivaandax wrote:
If all the x_i are positive real integers, then x_i can only equal one right???
Did you mean to write positive reals instead of positive integers?
thanks ,I edited
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