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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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[*]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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Minimum number of points
Ecrin_eren   2
N 2 hours ago by Shan3t
There are 18 teams in a football league. Each team plays against every other team twice in a season—once at home and once away. A win gives 3 points, a draw gives 1 point, and a loss gives 0 points. One team became the champion by earning more points than every other team. What is the minimum number of points this team could have?

2 replies
Ecrin_eren
Today at 4:09 PM
Shan3t
2 hours ago
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Weird locus problem
Sedro   7
N 2 hours ago by ReticulatedPython
Points $A$ and $B$ are in the coordinate plane such that $AB=2$. Let $\mathcal{H}$ denote the locus of all points $P$ in the coordinate plane satisfying $PA\cdot PB=2$, and let $M$ be the midpoint of $AB$. Points $X$ and $Y$ are on $\mathcal{H}$ such that $\angle XMY = 45^\circ$ and $MX\cdot MY=\sqrt{2}$. The value of $MX^4 + MY^4$ can be expressed in the form $\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
7 replies
Sedro
May 11, 2025
ReticulatedPython
2 hours ago
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Fond all functions in M with a) f(1)=5/2, b) f(1)=√3
Amir Hossein   5
N 3 hours ago by jasperE3
Source: IMO LongList 1982 - P34
Let $M$ be the set of all functions $f$ with the following properties:

(i) $f$ is defined for all real numbers and takes only real values.

(ii) For all $x, y \in \mathbb R$ the following equality holds: $f(x)f(y) = f(x + y) + f(x - y).$

(iii) $f(0) \neq 0.$

Determine all functions $f \in M$ such that

(a) $f(1)=\frac 52$,

(b) $f(1)= \sqrt 3$.
5 replies
Amir Hossein
Mar 18, 2011
jasperE3
3 hours ago
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help me please
thuanz123   6
N 4 hours ago by pavel kozlov
find all $a,b \in \mathbb{Z}$ such that:
a) $3a^2-2b^2=1$
b) $a^2-6b^2=1$
6 replies
thuanz123
Jan 17, 2016
pavel kozlov
4 hours ago
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Problem 5 (Second Day)
darij grinberg   78
N 4 hours ago by cj13609517288
Source: IMO 2004 Athens
In a convex quadrilateral $ABCD$, the diagonal $BD$ bisects neither the angle $ABC$ nor the angle $CDA$. The point $P$ lies inside $ABCD$ and satisfies \[\angle PBC=\angle DBA\quad\text{and}\quad \angle PDC=\angle BDA.\] Prove that $ABCD$ is a cyclic quadrilateral if and only if $AP=CP$.
78 replies
darij grinberg
Jul 13, 2004
cj13609517288
4 hours ago
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concyclic wanted, PQ = BP, cyclic quadrilateral and 2 parallelograms related
parmenides51   2
N 4 hours ago by SuperBarsh
Source: 2011 Italy TST 2.2
Let $ABCD$ be a cyclic quadrilateral in which the lines $BC$ and $AD$ meet at a point $P$. Let $Q$ be the point of the line $BP$, different from $B$, such that $PQ = BP$. We construct the parallelograms $CAQR$ and $DBCS$. Prove that the points $C, Q, R, S$ lie on the same circle.
2 replies
parmenides51
Sep 25, 2020
SuperBarsh
4 hours ago
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Integer FE Again
popcorn1   43
N 4 hours ago by DeathIsAwe
Source: ISL 2020 N5
Determine all functions $f$ defined on the set of all positive integers and taking non-negative integer values, satisfying the three conditions:
[list]
[*] $(i)$ $f(n) \neq 0$ for at least one $n$;
[*] $(ii)$ $f(x y)=f(x)+f(y)$ for every positive integers $x$ and $y$;
[*] $(iii)$ there are infinitely many positive integers $n$ such that $f(k)=f(n-k)$ for all $k<n$.
[/list]
43 replies
popcorn1
Jul 20, 2021
DeathIsAwe
4 hours ago
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2024 Mock AIME 1 ** p15 (cheaters' trap) - 128 | n^{\sigma (n)} - \sigma(n^n)
parmenides51   3
N 4 hours ago by Sedro
Let $N$ be the number of positive integers $n$ such that $n$ divides $2024^{2024}$ and $128$ divides
$$n^{\sigma (n)} - \sigma(n^n)$$where $\sigma (n)$ denotes the number of positive integers that divide $n$, including $1$ and $n$. Find the remainder when $N$ is divided by $1000$.
3 replies
1 viewing
parmenides51
Jan 29, 2025
Sedro
4 hours ago
J
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Long and wacky inequality
Royal_mhyasd   2
N 4 hours ago by Royal_mhyasd
Source: Me
Let $x, y, z$ be positive real numbers such that $x^2 + y^2 + z^2 = 12$. Find the minimum value of the following sum :
$$\sum_{cyc}\frac{(x^3+2y)^3}{3x^2yz - 16z - 8yz + 6x^2z}$$knowing that the denominators are positive real numbers.
2 replies
Royal_mhyasd
May 12, 2025
Royal_mhyasd
4 hours ago
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Perpendicular passes from the intersection of diagonals, \angle AEB = \angle CED
NO_SQUARES   1
N 4 hours ago by mathuz
Source: 239 MO 2025 10-11 p3
Inside of convex quadrilateral $ABCD$ point $E$ was chosen such that $\angle DAE = \angle CAB$ and $\angle ADE = \angle CDB$. Prove that if perpendicular from $E$ to $AD$ passes from the intersection of diagonals of $ABCD$, then $\angle AEB = \angle CED$.
1 reply
NO_SQUARES
May 5, 2025
mathuz
4 hours ago
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A game with balls and boxes
egxa   6
N 5 hours ago by Sh309had
Source: Turkey JBMO TST 2023 Day 1 P4
Initially, Aslı distributes $1000$ balls to $30$ boxes as she wishes. After that, Aslı and Zehra make alternated moves which consists of taking a ball in any wanted box starting with Aslı. One who takes the last ball from any box takes that box to herself. What is the maximum number of boxes can Aslı guarantee to take herself regardless of Zehra's moves?
6 replies
egxa
Apr 30, 2023
Sh309had
5 hours ago
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Angle Relationships in Triangles
steven_zhang123   2
N 5 hours ago by Captainscrubz
In $\triangle ABC$, $AB > AC$. The internal angle bisector of $\angle BAC$ and the external angle bisector of $\angle BAC$ intersect the ray $BC$ at points $D$ and $E$, respectively. Given that $CE - CD = 2AC$, prove that $\angle ACB = 2\angle ABC$.
2 replies
steven_zhang123
Yesterday at 11:09 PM
Captainscrubz
5 hours ago
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Easy functional equation
fattypiggy123   14
N 5 hours ago by Fly_into_the_sky
Source: Singapore Mathematical Olympiad 2014 Problem 2
Find all functions from the reals to the reals satisfying
\[f(xf(y) + x) = xy + f(x)\]
14 replies
fattypiggy123
Jul 5, 2014
Fly_into_the_sky
5 hours ago
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IOQM P23 2024
SomeonecoolLovesMaths   3
N 5 hours ago by lakshya2009
Consider the fourteen numbers, $1^4,2^4,...,14^4$. The smallest natural numebr $n$ such that they leave distinct remainders when divided by $n$ is:
3 replies
SomeonecoolLovesMaths
Sep 8, 2024
lakshya2009
5 hours ago
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Roots
phiReKaLk6781   2
N Apr 13, 2025 by lpieleanu
Give the positive root(s) of $ x^3 + 2x^2 - 2x - 4$.
2 replies
phiReKaLk6781
Mar 16, 2010
lpieleanu
Apr 13, 2025
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phiReKaLk6781
2074 posts
phiReKaLk6781
#1 h  Mar 16, 2010, 10:29 PM • 3 Y
Y by Adventure10 and 2 other users
Give the positive root(s) of $ x^3 + 2x^2 - 2x - 4$.
This post has been edited 1 time. Last edited by phiReKaLk6781, Mar 16, 2010, 10:48 PM
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mismatchtea
260 posts
mismatchtea
#2 h  Mar 16, 2010, 10:44 PM • 2 Y
Y by Adventure10, Mango247
Solution
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lpieleanu
3001 posts
lpieleanu
#3 h  Apr 13, 2025, 12:10 AM
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