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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 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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Combinatorial proof
MathBot101101   10
N 18 minutes ago by MathBot101101
Is there a way to prove
\frac{1}{(1+1)!}+\frac{2}{(2+1)!}+...+\frac{n}{(n+1)!}=1-\frac{1}{{n+1)!}
without induction and using only combinatorial arguments?

Induction proof wasn't quite as pleasing for me.
10 replies
MathBot101101
Apr 20, 2025
MathBot101101
18 minutes ago
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Inequalities
sqing   13
N 26 minutes ago by sqing
Let $ a,b,c> 0 $ and $ ab+bc+ca\leq 3abc . $ Prove that
$$ a+ b^2+c\leq a^2+ b^3+c^2 $$$$ a+ b^{11}+c\leq a^2+ b^{12}+c^2 $$
13 replies
sqing
Yesterday at 1:54 PM
sqing
26 minutes ago
J
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Simiplifying a Complicated Expression
phiReKaLk6781   6
N an hour ago by lbh_qys
Simplify: $ \frac{a^3}{(a-b)(a-c)}+\frac{b^3}{(b-a)(b-c)}+\frac{c^3}{(c-a)(c-b)}$
6 replies
phiReKaLk6781
Mar 15, 2010
lbh_qys
an hour ago
J
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Easy Number Theory
math_comb01   37
N an hour ago by John_Mgr
Source: INMO 2024/3
Let $p$ be an odd prime and $a,b,c$ be integers so that the integers $$a^{2023}+b^{2023},\quad b^{2024}+c^{2024},\quad a^{2025}+c^{2025}$$are divisible by $p$.
Prove that $p$ divides each of $a,b,c$.
$\quad$
Proposed by Navilarekallu Tejaswi
37 replies
math_comb01
Jan 21, 2024
John_Mgr
an hour ago
J
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ALGEBRA INEQUALITY
Tony_stark0094   3
N an hour ago by sqing
$a,b,c > 0$ Prove that $$\frac{a^2+bc}{b+c} + \frac{b^2+ac}{a+c} + \frac {c^2 + ab}{a+b} \geq a+b+c$$
3 replies
Tony_stark0094
Today at 12:17 AM
sqing
an hour ago
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Inspired by hlminh
sqing   3
N an hour ago by sqing
Source: Own
Let $ a,b,c $ be real numbers such that $ a^2+b^2+c^2=1. $ Prove that $$ |a-kb|+|b-kc|+|c-ka|\leq \sqrt{3k^2+2k+3}$$Where $ k\geq 0 . $
3 replies
sqing
Yesterday at 4:43 AM
sqing
an hour ago
J
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A Familiar Point
v4913   51
N an hour ago by xeroxia
Source: EGMO 2023/6
Let $ABC$ be a triangle with circumcircle $\Omega$. Let $S_b$ and $S_c$ respectively denote the midpoints of the arcs $AC$ and $AB$ that do not contain the third vertex. Let $N_a$ denote the midpoint of arc $BAC$ (the arc $BC$ including $A$). Let $I$ be the incenter of $ABC$. Let $\omega_b$ be the circle that is tangent to $AB$ and internally tangent to $\Omega$ at $S_b$, and let $\omega_c$ be the circle that is tangent to $AC$ and internally tangent to $\Omega$ at $S_c$. Show that the line $IN_a$, and the lines through the intersections of $\omega_b$ and $\omega_c$, meet on $\Omega$.
51 replies
v4913
Apr 16, 2023
xeroxia
an hour ago
J
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Apple sharing in Iran
mojyla222   3
N 2 hours ago by math-helli
Source: Iran 2025 second round p6
Ali is hosting a large party. Together with his $n-1$ friends, $n$ people are seated around a circular table in a fixed order. Ali places $n$ apples for serving directly in front of himself and wants to distribute them among everyone. Since Ali and his friends dislike eating alone and won't start unless everyone receives an apple at the same time, in each step, each person who has at least one apple passes one apple to the first person to their right who doesn't have an apple (in the clockwise direction).

Find all values of $n$ such that after some number of steps, the situation reaches a point where each person has exactly one apple.
3 replies
mojyla222
Apr 20, 2025
math-helli
2 hours ago
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Iran second round 2025-q1
mohsen   5
N 2 hours ago by math-helli
Find all positive integers n>2 such that sum of n and any of its prime divisors is a perfect square.
5 replies
mohsen
Apr 19, 2025
math-helli
2 hours ago
J
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Iran Team Selection Test 2016
MRF2017   9
N 2 hours ago by SimplisticFormulas
Source: TST3,day1,P2
Let $ABC$ be an arbitrary triangle and $O$ is the circumcenter of $\triangle {ABC}$.Points $X,Y$ lie on $AB,AC$,respectively such that the reflection of $BC$ WRT $XY$ is tangent to circumcircle of $\triangle {AXY}$.Prove that the circumcircle of triangle $AXY$ is tangent to circumcircle of triangle $BOC$.
9 replies
MRF2017
Jul 15, 2016
SimplisticFormulas
2 hours ago
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How many ways can we indistribute n different marbles into 6 identical boxes
Taiharward   4
N 3 hours ago by Taiharward
How many ways can we distribute n indifferent marbles into 6 identical boxes and one jar?
4 replies
Taiharward
4 hours ago
Taiharward
3 hours ago
J
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Combo problem
soryn   3
N 4 hours ago by soryn
The school A has m1 boys and m2 girls, and ,the school B has n1 boys and n2 girls. Each school is represented by one team formed by p students,boys and girls. If f(k) is the number of cases for which,the twice schools has,togheter k girls, fund f(k) and the valute of k, for which f(k) is maximum.
3 replies
soryn
Yesterday at 6:33 AM
soryn
4 hours ago
J
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Looking for the smallest ghost
Justpassingby   5
N 4 hours ago by venhancefan777
Source: 2021 Mexico Center Zone Regional Olympiad, problem 1
Let $p$ be an odd prime number. Let $S=a_1,a_2,\dots$ be the sequence defined as follows: $a_1=1,a_2=2,\dots,a_{p-1}=p-1$, and for $n\ge p$, $a_n$ is the smallest integer greater than $a_{n-1}$ such that in $a_1,a_2,\dots,a_n$ there are no arithmetic progressions of length $p$. We say that a positive integer is a ghost if it doesn’t appear in $S$.
What is the smallest ghost that is not a multiple of $p$?

Proposed by Guerrero
5 replies
Justpassingby
Jan 17, 2022
venhancefan777
4 hours ago
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non-symmetric ineq (for girls)
easternlatincup   36
N 4 hours ago by Tony_stark0094
Source: Chinese Girl's MO 2007
For $ a,b,c\geq 0$ with $ a+b+c=1$, prove that

$ \sqrt{a+\frac{(b-c)^2}{4}}+\sqrt{b}+\sqrt{c}\leq \sqrt{3}$
36 replies
easternlatincup
Dec 30, 2007
Tony_stark0094
4 hours ago
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Counting Prime Numbers
phiReKaLk6781   2
N Apr 13, 2025 by lpieleanu
How many primes exist which are less than 50?
2 replies
phiReKaLk6781
Mar 16, 2010
lpieleanu
Apr 13, 2025
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Counting Prime Numbers
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Reveal topic tags
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phiReKaLk6781
2074 posts
phiReKaLk6781
#1 h  Mar 16, 2010, 10:29 PM • 4 Y
Y by Adventure10 and 3 other users
How many primes exist which are less than 50?
This post has been edited 1 time. Last edited by phiReKaLk6781, Mar 16, 2010, 10:49 PM
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isabella2296
4829 posts
isabella2296
#2 h  Mar 16, 2010, 10:42 PM • 2 Y
Y by Adventure10, Mango247
We can just count: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. $ 15$ in all.
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lpieleanu
2911 posts
lpieleanu
#3 h  Apr 13, 2025, 12:08 AM
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