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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)!

Be sure to mark your calendars for the following upcoming events:
[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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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
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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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Serbian selection contest for the IMO 2025 - P2
OgnjenTesic   8
N 10 minutes ago by MathLuis
Source: Serbian selection contest for the IMO 2025
Let $ABC$ be an acute triangle. Let $A'$ be the reflection of point $A$ over the line $BC$. Let $O$ and $H$ be the circumcenter and the orthocenter of triangle $ABC$, respectively, and let $E$ be the midpoint of segment $OH$. Let $D$ and $L$ be the points where the reflection of line $AA'$ with respect to line $OA'$ intersects the circumcircle of triangle $ABC$, where point $D$ lies on the arc $BC$ not containing $A$. If \( M \) is a point on the line \( BC \) such that \( OM \perp AD \), prove that \( \angle MAD = \angle EAL \).

Proposed by Strahinja Gvozdić
8 replies
OgnjenTesic
Today at 4:02 PM
MathLuis
10 minutes ago
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Primes and sets
mathisreaI   41
N 34 minutes ago by Tinoba-is-emotional
Source: IMO 2022 Problem 3
Let $k$ be a positive integer and let $S$ be a finite set of odd prime numbers. Prove that there is at most one way (up to rotation and reflection) to place the elements of $S$ around the circle such that the product of any two neighbors is of the form $x^2+x+k$ for some positive integer $x$.
41 replies
mathisreaI
Jul 13, 2022
Tinoba-is-emotional
34 minutes ago
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Minimum times maximum
y-is-the-best-_   64
N 35 minutes ago by ezpotd
Source: IMO 2019 SL A2
Let $u_1, u_2, \dots, u_{2019}$ be real numbers satisfying \[u_{1}+u_{2}+\cdots+u_{2019}=0 \quad \text { and } \quad u_{1}^{2}+u_{2}^{2}+\cdots+u_{2019}^{2}=1.\]Let $a=\min \left(u_{1}, u_{2}, \ldots, u_{2019}\right)$ and $b=\max \left(u_{1}, u_{2}, \ldots, u_{2019}\right)$. Prove that
\[ a b \leqslant-\frac{1}{2019}. \]
64 replies
y-is-the-best-_
Sep 22, 2020
ezpotd
35 minutes ago
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Prove $x+y$ is a composite number.
mt0204   1
N an hour ago by sharknavy75
Let $x, y \in \mathbb{N}^*$ such that $1000 x^{2023}+2024 y^{2023}$ is divisible by $x+y$ and $x+y>2$. Prove that $x+y$ is a composite number.
1 reply
mt0204
Today at 3:59 PM
sharknavy75
an hour ago
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p^3-q^3=pq^3-1
parmenides51   3
N Yesterday at 12:04 PM by Assassino9931
Source: 2016 Belarus TST 1.3
Solve the equation $p^3-q^3=pq^3-1$ in primes $p,q$.
3 replies
parmenides51
Nov 4, 2020
Assassino9931
Yesterday at 12:04 PM
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Israel Number Theory
mathisreaI   67
N May 20, 2025 by lolsamo
Source: IMO 2022 Problem 5
Find all triples $(a,b,p)$ of positive integers with $p$ prime and \[ a^p=b!+p. \]
67 replies
mathisreaI
Jul 13, 2022
lolsamo
May 20, 2025
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1998 KJMO P1 Finding integer solutions(easy)
RL_parkgong_0106   2
N May 19, 2025 by JH_K2IMO
Source: 1998 KJMO P1
Show that there exist no integer solutions $(x, y, z)$ to the equation

$$x^3+2y^3+4z^3=9$$
2 replies
RL_parkgong_0106
Jun 30, 2024
JH_K2IMO
May 19, 2025
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3^x+4xy=5^y diophantine
parmenides51   8
N May 18, 2025 by shendrew7
Source: 2020 ℕumber Theory Contest (USAJMO level) #1 https://artofproblemsolving.com/community/c594864h2339943p18855098
Find all ordered pairs of natural numbers $(x,y)$ such that$$3^x+4xy=5^y.$$
Proposed by i3435
8 replies
parmenides51
Dec 3, 2023
shendrew7
May 18, 2025
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A diophantine equation
crazyfehmy   14
N May 18, 2025 by MathIQ.
Source: Turkey Junior National Olympiad 2012 P1
Let $x, y$ be integers and $p$ be a prime for which

\[ x^2-3xy+p^2y^2=12p \]
Find all triples $(x,y,p)$.
14 replies
crazyfehmy
Dec 12, 2012
MathIQ.
May 18, 2025
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Polish MO Finals 2014, Problem 5
j___d   14
N May 17, 2025 by Kempu33334
Source: Polish MO Finals 2014
Find all pairs $(x,y)$ of positive integers that satisfy
$$2^x+17=y^4$$.
14 replies
j___d
Jul 27, 2016
Kempu33334
May 17, 2025
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Pythagorean Diophantine?
youochange   1
N May 17, 2025 by tom-nowy
The number of ordered pair $(a,b)$ of positive integers with $a \le b$ satisfying $a^2+b^2=2025$ is

Click to reveal hidden text
1 reply
youochange
May 17, 2025
tom-nowy
May 17, 2025
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Find all integers satisfying this equation
Sadigly   2
N May 13, 2025 by ilovenumbertheories
Source: Azerbaijan NMO 2019
Find all $x;y\in\mathbb{Z}$ satisfying the following condition: $$x^3=y^4+9x^2$$
2 replies
Sadigly
May 11, 2025
ilovenumbertheories
May 13, 2025
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Diophantine involving cube
Sadigly   2
N May 12, 2025 by Adywastaken
Source: Azerbaijan Senior NMO 2020
$a;b;c;d\in\mathbb{Z^+}$. Solve the equation: $$2^{a!}+2^{b!}+2^{c!}=d^3$$
2 replies
Sadigly
May 11, 2025
Adywastaken
May 12, 2025
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Classic Diophantine
Adywastaken   4
N May 10, 2025 by mrtheory
Source: NMTC 2024/6
Find all natural number solutions to $3^x-5^y=z^2$.
4 replies
Adywastaken
May 10, 2025
mrtheory
May 10, 2025
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ez problem....
Cobedangiu   2
N Apr 21, 2025 by Cobedangiu
problem solved
2 replies
Cobedangiu
Apr 21, 2025
Cobedangiu
Apr 21, 2025
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ez problem....
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Reveal topic tags
inequalities
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Cobedangiu
70 posts
Cobedangiu
#1 h  Apr 21, 2025, 10:54 AM
Y by
problem solved
This post has been edited 3 times. Last edited by Cobedangiu, May 2, 2025, 3:09 AM
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arqady
30256 posts
arqady
#2 h  Apr 21, 2025, 11:48 AM
Y by
Cobedangiu wrote:
let $a,b,c$ be the lengths of the sides of the triangle. Prove that:
$(a+b+c)(\dfrac{3a-b}{a^2+ab}+\dfrac{3b-c}{b^2+bc}+\dfrac{3c-a}{c^2+ac})\le 9$
It's true for any positive variables.
Z K Y
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Cobedangiu
70 posts
Cobedangiu
#3 h  Apr 21, 2025, 1:26 PM
Y by
arqady wrote:
Cobedangiu wrote:
let $a,b,c$ be the lengths of the sides of the triangle. Prove that:
$(a+b+c)(\dfrac{3a-b}{a^2+ab}+\dfrac{3b-c}{b^2+bc}+\dfrac{3c-a}{c^2+ac})\le 9$
It's true for any positive variables.

yes -)
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