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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.

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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
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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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Interesting inequalities
sqing   0
4 minutes ago
Source: Own
Let $ a,b,c\geq 0 , a(b+c)=k.$ Prove that
$$\frac{1}{a+1}+\frac{2}{b+1}+\frac{1}{c+1}\geq \frac{4\sqrt{k}-6}{ k-2}$$Where $5\leq k\in N^+.$
Let $ a,b,c\geq 0 , a(b+c)=9.$ Prove that
$$\frac{1}{a+1}+\frac{2}{b+1}+\frac{1}{c+1}\geq \frac{6}{7}$$
0 replies
1 viewing
sqing
4 minutes ago
0 replies
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k^2/p for k =1 to (p-1)/2
truongphatt2668   0
6 minutes ago
Let $p$ be a prime such that: $p = 4k+1$. Simplify:
$$\sum_{k=1}^{\frac{p-1}{2}}\begin{Bmatrix}\dfrac{k^2}{p}\end{Bmatrix}$$
0 replies
truongphatt2668
6 minutes ago
0 replies
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Interesting inequalities
sqing   1
N 24 minutes ago by sqing
Source: Own
Let $ a,b,c\geq 0 , ab+bc+kca =k+2.$ Prove that
$$\frac{1}{a+1}+\frac{2}{b+1}+\frac{1}{c+1}\geq \frac{k^2+k+2+2k\sqrt{k+2}}{(k+1)^2}$$Where $ k\in N^+.$
Let $ a,b,c\geq 0 , ab+bc+ca =3.$ Prove that
$$\frac{1}{a+1}+\frac{2}{b+1}+\frac{1}{c+1}\geq 1+\frac{\sqrt 3}{2}$$Let $ a,b,c\geq 0 , ab+bc+2ca =4.$ Prove that
$$\frac{1}{a+1}+\frac{2}{b+1}+\frac{1}{c+1}\geq \frac{16}{9}$$
1 reply
1 viewing
sqing
27 minutes ago
sqing
24 minutes ago
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Non-homogeneous degree 3 inequality
Lukaluce   3
N 25 minutes ago by Sh309had
Source: 2024 Junior Macedonian Mathematical Olympiad P1
Let $a, b$, and $c$ be positive real numbers. Prove that
\[\frac{a^4 + 3}{b} + \frac{b^4 + 3}{c} + \frac{c^4 + 3}{a} \ge 12.\]When does equality hold?

Proposed by Petar Filipovski
3 replies
Lukaluce
Apr 14, 2025
Sh309had
25 minutes ago
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Distinct Integers with Divisibility Condition
tastymath75025   17
N 31 minutes ago by quantam13
Source: 2017 ELMO Shortlist N3
For each integer $C>1$ decide whether there exist pairwise distinct positive integers $a_1,a_2,a_3,...$ such that for every $k\ge 1$, $a_{k+1}^k$ divides $C^ka_1a_2...a_k$.

Proposed by Daniel Liu
17 replies
tastymath75025
Jul 3, 2017
quantam13
31 minutes ago
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IMO 2011 Problem 1
Amir Hossein   102
N 32 minutes ago by Jupiterballs
Given any set $A = \{a_1, a_2, a_3, a_4\}$ of four distinct positive integers, we denote the sum $a_1 +a_2 +a_3 +a_4$ by $s_A$. Let $n_A$ denote the number of pairs $(i, j)$ with $1 \leq i < j \leq 4$ for which $a_i +a_j$ divides $s_A$. Find all sets $A$ of four distinct positive integers which achieve the largest possible value of $n_A$.

Proposed by Fernando Campos, Mexico
102 replies
Amir Hossein
Jul 18, 2011
Jupiterballs
32 minutes ago
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harmonic quadrilateral
Lukariman   2
N 33 minutes ago by Lukariman
Given quadrilateral ABCD inscribed in a circle with center O. CA:CB= DA:DB are satisfied. M is any point and d is a line parallel to MC. Radial projection M transforms A,B,D onto line d into A',B',D'. Prove that B' is the midpoint of A'D'.
2 replies
Lukariman
Today at 6:36 AM
Lukariman
33 minutes ago
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Find the angle alpha [Iran Second Round 1994]
Amir Hossein   4
N 35 minutes ago by Mysteriouxxx
In the following diagram, $O$ is the center of the circle. If three angles $\alpha, \beta$ and $\gamma$ be equal, find $\alpha.$
IMAGE
4 replies
Amir Hossein
Nov 26, 2010
Mysteriouxxx
35 minutes ago
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Inequality
lgx57   1
N 41 minutes ago by DAVROS
Source: Own
$a,b>0$,$a^4+a^2b^2+b^4=k$.Find the min of $4a^2-ab+4b^2$.

$a,b>0$,$a^4-a^2b^2+b^4=k$.Find the min of $4a^2-ab+4b^2$.
1 reply
lgx57
5 hours ago
DAVROS
41 minutes ago
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Calculating sum of the numbers
Sadigly   2
N an hour ago by Gggvds1
Source: Azerbaijan Junior MO 2025 P4
A $3\times3$ square is filled with numbers $1;2;3...;9$.The numbers inside four $2\times2$ squares is summed,and arranged in an increasing order. Is it possible to obtain the following sequences as a result of this operation?

$\text{a)}$ $24,24,25,25$

$\text{b)}$ $20,23,26,29$
2 replies
Sadigly
Today at 7:56 AM
Gggvds1
an hour ago
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Help me identify what should i focus in alcumus for contest's each problem
Hope_and_fight   0
an hour ago

So this file i have attached is a sample test from my upcoming regional schools' math contest. This is just a test sample, i was looking for problems as similar as to these so i have more material to practice with. Unfortunately i don't have much time to read the whole books the contest is already soon. I want to test myself as much as possible with problems, also Alcumus shows from what section of the book it is. so i can kinda cram the pages

TLDR: I WOULD BE REALLY GRATEFUL IF YOU COULD POINT ON WHAT TO FOCUS ON ALCUMUS FOR EACH OF THESE CONTEST PROBLEMS. AND SORRY FOR MY ENGLISH. I DON'T KNOW MUCH OF MATH IN THERE:)
0 replies
Hope_and_fight
an hour ago
0 replies
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Divisibility..
Sadigly   1
N an hour ago by Mathzeus1024
Source: Azerbaijan Junior MO 2025 P2
Find all $4$ consecutive even numbers, such that the square of their product is divisible by the sum of their squares.
1 reply
Sadigly
Today at 7:37 AM
Mathzeus1024
an hour ago
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official solution of IGO
ABCD1728   7
N 2 hours ago by ABCD1728
Source: IGO official website
Where can I get the official solution of IGO for 2023 and 2024, there are some inhttps://imogeometry.blogspot.com/p/iranian-geometry-olympiad.html, but where can I find them on the official website, thanks :)
7 replies
ABCD1728
May 4, 2025
ABCD1728
2 hours ago
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Combo geo with circles
a_507_bc   10
N 2 hours ago by EthanWYX2009
Source: 239 MO 2024 S8
There are $2n$ points on the plane. No three of them lie on the same straight line and no four lie on the same circle. Prove that it is possible to split these points into $n$ pairs and cover each pair of points with a circle containing no other points.
10 replies
a_507_bc
May 22, 2024
EthanWYX2009
2 hours ago
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\pi(n) is a good divisor
sefatod628   1
N Apr 26, 2025 by kiyoras_2001
Source: unknown/given at a math club
Prove that there is an infinity of $n\in \mathbb{N^*}$ such that $\pi(n) \mid n$.

Hint :Click to reveal hidden text
1 reply
sefatod628
Apr 25, 2025
kiyoras_2001
Apr 26, 2025
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\pi(n) is a good divisor
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Reveal topic tags
number theory
number theory solved
number theory theorems
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Source: unknown/given at a math club
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sefatod628
23 posts
sefatod628
#1 h  Apr 25, 2025, 2:37 PM
Y by
Prove that there is an infinity of $n\in \mathbb{N^*}$ such that $\pi(n) \mid n$.

Hint :Click to reveal hidden text
This post has been edited 1 time. Last edited by sefatod628, Apr 25, 2025, 2:38 PM
Reason: typo
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kiyoras_2001
678 posts
kiyoras_2001
#2 h  Apr 26, 2025, 10:27 AM
Y by
This is old. See Iran 2002.
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