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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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[*]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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k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
J
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k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
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A sharp one with 4 var
mihaig   0
12 minutes ago
Source: Own
Let $a,b,c,d\geq0$ satisfying
$$\left(a+b+c+d-1\right)^2+7\leq\frac83\cdot\left(ab+bc+ca+ad+bd+cd\right).$$Prove
$$\frac1{a+1}+\frac1{b+1}+\frac1{c+1}+\frac1{d+1}\leq2.$$
0 replies
mihaig
12 minutes ago
0 replies
J
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A geometry problem
Lttgeometry   0
15 minutes ago
Triangle $ABC$ has two isogonal conjugate points $P$ and $Q$. The circle $(BPC)$ intersects circle $(AP)$ at $R \neq A$, and the circle $(BQC)$ intersects circle $(AQ)$ at $S\neq A$. Prove that $R$ and $S$ are isogonal conjugates in triangle $ABC$.
Note: Circle $(AP)$ is the circle with diameter $AP$, Circle $(AQ)$ is the circle with diameter $AQ$.
0 replies
Lttgeometry
15 minutes ago
0 replies
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A sharp one with 3 var
mihaig   9
N 19 minutes ago by mihaig
Source: Own
Let $a,b,c\geq0$ satisfying
$$\left(a+b+c-2\right)^2+8\leq3\left(ab+bc+ca\right).$$Prove
$$ab+bc+ca+abc\geq4.$$
9 replies
mihaig
May 13, 2025
mihaig
19 minutes ago
J
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Van der Corput Inequality
EthanWYX2009   0
42 minutes ago
Source: en.wikipedia.org/wiki/Van_der_Corput_inequality
Let $V$ be a real or complex inner product space. Suppose that ${\displaystyle v,u_{1},\dots ,u_{n}\in V} $ and that ${\displaystyle \|v\|=1}.$ Then$${\displaystyle \displaystyle \left(\sum _{i=1}^{n}|\langle v,u_{i}\rangle |\right)^{2}\leq \sum _{i,j=1}^{n}|\langle u_{i},u_{j}\rangle |.}$$
0 replies
EthanWYX2009
42 minutes ago
0 replies
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Hard Functional Equation in the Complex Numbers
yaybanana   6
N an hour ago by jasperE3
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 $x,y \in \mathbb{C}$
6 replies
yaybanana
Apr 9, 2025
jasperE3
an hour ago
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FE with conditions on $x,y$
Adywastaken   3
N an hour ago by jasperE3
Source: OAO
Find all functions $f:\mathbb{R_{+}}\rightarrow \mathbb{R_{+}}$ such that $\forall y>x>0$,
\[ f(x^2+f(y))=f(xf(x))+y \]
3 replies
Adywastaken
Friday at 6:18 PM
jasperE3
an hour ago
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Point satisfies triple property
62861   36
N an hour ago by cursed_tangent1434
Source: USA Winter Team Selection Test #2 for IMO 2018, Problem 2
Let $ABCD$ be a convex cyclic quadrilateral which is not a kite, but whose diagonals are perpendicular and meet at $H$. Denote by $M$ and $N$ the midpoints of $\overline{BC}$ and $\overline{CD}$. Rays $MH$ and $NH$ meet $\overline{AD}$ and $\overline{AB}$ at $S$ and $T$, respectively. Prove that there exists a point $E$, lying outside quadrilateral $ABCD$, such that
[list]
[*] ray $EH$ bisects both angles $\angle BES$, $\angle TED$, and
[*] $\angle BEN = \angle MED$.
[/list]

Proposed by Evan Chen
36 replies
62861
Jan 22, 2018
cursed_tangent1434
an hour ago
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Inspired by 2025 Xinjiang
sqing   1
N 2 hours ago by sqing
Source: Own
Let $ a,b,c >0 . $ Prove that
$$ \left(1+\frac {a} { b}\right)\left(2+\frac {a}{ b}+\frac {b}{ c}\right) \left(1+\frac {a}{b}+\frac {b}{ c}+\frac {c}{ a}\right) \geq 12+8\sqrt 2 $$
1 reply
sqing
Yesterday at 5:32 PM
sqing
2 hours ago
J
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Inspired by 2025 Beijing
sqing   4
N 2 hours ago by pooh123
Source: Own
Let $ a,b,c,d >0 $ and $ (a^2+b^2+c^2)(b^2+c^2+d^2)=36. $ Prove that
$$ab^2c^2d \leq 8$$$$a^2bcd^2 \leq 16$$$$ ab^3c^3d \leq \frac{2187}{128}$$$$ a^3bcd^3 \leq \frac{2187}{32}$$
4 replies
sqing
Yesterday at 4:56 PM
pooh123
2 hours ago
J
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Find the minimum
sqing   27
N 2 hours ago by sqing
Source: Zhangyanzong
Let $a,b$ be positive real numbers such that $a^2b^2+\frac{4a}{a+b}=4.$ Find the minimum value of $a+2b.$
27 replies
sqing
Sep 4, 2018
sqing
2 hours ago
J
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Sharygin 2025 CR P15
Gengar_in_Galar   7
N 2 hours ago by Giant_PT
Source: Sharygin 2025
A point $C$ lies on the bisector of an acute angle with vertex $S$. Let $P$, $Q$ be the projections of $C$ to the sidelines of the angle. The circle centered at $C$ with radius $PQ$ meets the sidelines at points $A$ and $B$ such that $SA\ne SB$. Prove that the circle with center $A$ touching $SB$ and the circle with center $B$ touching $SA$ are tangent.
Proposed by: A.Zaslavsky
7 replies
Gengar_in_Galar
Mar 10, 2025
Giant_PT
2 hours ago
J
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Inequality olympiad algebra
Foxellar   1
N 2 hours ago by sqing
Given that \( a, b, c \) are nonzero real numbers such that
\[ \frac{1}{abc} + \frac{1}{a} + \frac{1}{c} = \frac{1}{b}, \]let \( M \) be the maximum value of the expression
\[ \frac{4}{a^2 + 1} + \frac{4}{b^2 + 1} + \frac{7}{c^2 + 1}. \]Determine the sum of the numerator and denominator of the simplified fraction representing \( M \).
1 reply
Foxellar
Yesterday at 10:01 PM
sqing
2 hours ago
J
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Inspired by RMO 2006
sqing   2
N 2 hours ago by sqing
Source: Own
Let $ a,b >0 . $ Prove that
$$ \frac {a^{2}+1}{b+k}+\frac { b^{2}+1}{ka+1}+\frac {2}{a+kb} \geq \frac {6}{k+1} $$Where $k\geq 0.03 $
$$ \frac {a^{2}+1}{b+1}+\frac { b^{2}+1}{a+1}+\frac {2}{a+b} \geq 3 $$
2 replies
sqing
Yesterday at 3:24 PM
sqing
2 hours ago
J
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Inspired by 2025 Xinjiang
sqing   3
N 2 hours ago by sqing
Source: Own
Let $ a,b >0 . $ Prove that
$$ \left(1+\frac {a} { b}\right)\left(6+\frac {b}{a}\right) \left(2+\frac {a}{b}+\frac {b}{ a}\right) \geq\frac {625}{ 12}$$$$ \left(1+\frac {a} { b}\right)\left(6+\frac {a}{b}\right) \left(2+\frac {a}{b}+\frac {b}{ a}\right) \geq29+6\sqrt 6$$$$ \left(1+\frac {a} { b}\right)\left(2+\frac {b}{ a}\right) \left(2+\frac {a}{b}+\frac {b}{ a}\right) \geq \frac{3(63+11\sqrt{33})}{16} $$$$ \left(1+\frac {a} { b}\right)\left(2+\frac {a}{ b}\right) \left(2+\frac {a}{b}+\frac {b}{ a}\right) \geq \frac{223+70\sqrt{10}}{27} $$
3 replies
sqing
Yesterday at 5:56 PM
sqing
2 hours ago
J
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J
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Functionnal equation
Rayanelba   1
N Apr 30, 2025 by Mrcuberoot
Source: Own
Find all functions $f:\mathbb{R}_{>0}\to \mathbb{R}_{>0}$ that verify the following equation for all $x,y\in \mathbb{R}_{>0}$:
$f(x+yf(x))+f(\frac{x}{y})=\frac{x}{y}+f(x+xy)$
1 reply
Rayanelba
Apr 30, 2025
Mrcuberoot
Apr 30, 2025
J
Functionnal equation
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Reveal topic tags
algebra
functional equation
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Source: Own
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Rayanelba
20 posts
Rayanelba
#1 h  Apr 30, 2025, 4:10 PM
Y by
Find all functions $f:\mathbb{R}_{>0}\to \mathbb{R}_{>0}$ that verify the following equation for all $x,y\in \mathbb{R}_{>0}$:
$f(x+yf(x))+f(\frac{x}{y})=\frac{x}{y}+f(x+xy)$
This post has been edited 2 times. Last edited by Rayanelba, Apr 30, 2025, 7:25 PM
Reason: Typo
Z K Y
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Mrcuberoot
28 posts
Mrcuberoot
#2 h  Apr 30, 2025, 6:27 PM • 2 Y
Y by Rayanelba, ATM_
Unsolvable probably
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