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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
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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 Familiar Point
v4913   52
N 35 minutes ago by SimplisticFormulas
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 $\Omega$.
52 replies
v4913
Apr 16, 2023
SimplisticFormulas
35 minutes ago
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Tangential quadrilateral and 8 lengths
popcorn1   72
N 39 minutes ago by cj13609517288
Source: IMO 2021 P4
Let $\Gamma$ be a circle with centre $I$, and $A B C D$ a convex quadrilateral such that each of the segments $A B, B C, C D$ and $D A$ is tangent to $\Gamma$. Let $\Omega$ be the circumcircle of the triangle $A I C$. The extension of $B A$ beyond $A$ meets $\Omega$ at $X$, and the extension of $B C$ beyond $C$ meets $\Omega$ at $Z$. The extensions of $A D$ and $C D$ beyond $D$ meet $\Omega$ at $Y$ and $T$, respectively. Prove that \[A D+D T+T X+X A=C D+D Y+Y Z+Z C.\]
Proposed by Dominik Burek, Poland and Tomasz Ciesla, Poland
72 replies
popcorn1
Jul 20, 2021
cj13609517288
39 minutes ago
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An algorithm for discovering prime numbers?
Lukaluce   3
N an hour ago by TopGbulliedU
Source: 2025 Junior Macedonian Mathematical Olympiad P3
Is there an infinite sequence of prime numbers $p_1, p_2, ..., p_n, ...,$ such that for every $i \in \mathbb{N}, p_{i + 1} \in \{2p_i - 1, 2p_i + 1\}$ is satisfied? Explain the answer.
3 replies
Lukaluce
May 18, 2025
TopGbulliedU
an hour ago
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Random concyclicity in a square config
Maths_VC   5
N an hour ago by Royal_mhyasd
Source: Serbia JBMO TST 2025, Problem 1
Let $M$ be a random point on the smaller arc $AB$ of the circumcircle of square $ABCD$, and let $N$ be the intersection point of segments $AC$ and $DM$. The feet of the tangents from point $D$ to the circumcircle of the triangle $OMN$ are $P$ and $Q$ , where $O$ is the center of the square. Prove that points $A$, $C$, $P$ and $Q$ lie on a single circle.
5 replies
Maths_VC
Tuesday at 7:38 PM
Royal_mhyasd
an hour ago
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Basic ideas in junior diophantine equations
Maths_VC   3
N an hour ago by Royal_mhyasd
Source: Serbia JBMO TST 2025, Problem 3
Determine all positive integers $a, b$ and $c$ such that
$2$ $\cdot$ $10^a + 5^b = 2025^c$
3 replies
Maths_VC
Tuesday at 7:54 PM
Royal_mhyasd
an hour ago
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Prime number theory
giangtruong13   2
N 2 hours ago by RagvaloD
Find all prime numbers $p,q$ such that: $p^2-pq-q^3=1$
2 replies
giangtruong13
2 hours ago
RagvaloD
2 hours ago
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Easy number theory
britishprobe17   34
N 2 hours ago by CJB19
The number of factors from 2024 that are greater than $\sqrt{2024}$ are
34 replies
britishprobe17
Oct 16, 2024
CJB19
2 hours ago
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Problem 2
delegat   147
N 2 hours ago by math-olympiad-clown
Source: 0
Let $n\ge 3$ be an integer, and let $a_2,a_3,\ldots ,a_n$ be positive real numbers such that $a_{2}a_{3}\cdots a_{n}=1$. Prove that
\[(1 + a_2)^2 (1 + a_3)^3 \dotsm (1 + a_n)^n > n^n.\]

Proposed by Angelo Di Pasquale, Australia
147 replies
delegat
Jul 10, 2012
math-olympiad-clown
2 hours ago
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Area of Polygon
AIME15   50
N 2 hours ago by Charizard_637
The area of polygon $ ABCDEF$, in square units, is

IMAGE

\[ \textbf{(A)}\ 24 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 46 \qquad \textbf{(D)}\ 66 \qquad \textbf{(E)}\ 74 \]
50 replies
AIME15
Jan 12, 2009
Charizard_637
2 hours ago
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Coloring points of a square, finding a monochromatic hexagon
goodar2006   6
N 2 hours ago by quantam13
Source: Iran 3rd round 2012-Special Lesson exam-Part 2-P1
Prove that for each coloring of the points inside or on the boundary of a square with $1391$ colors, there exists a monochromatic regular hexagon.
6 replies
goodar2006
Sep 15, 2012
quantam13
2 hours ago
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last 1000 digits
teomihai   2
N 2 hours ago by Charizard_637
prove :$ 2^{10000}+3^{10000}+5^{10000}<10^{10000}$
Generalization.
2 replies
teomihai
Today at 11:31 AM
Charizard_637
2 hours ago
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Van der Warden Theorem!
goodar2006   7
N 2 hours ago by quantam13
Source: Iran 3rd round 2012-Special Lesson exam-Part 2-P2
Suppose $W(k,2)$ is the smallest number such that if $n\ge W(k,2)$, for each coloring of the set $\{1,2,...,n\}$ with two colors there exists a monochromatic arithmetic progression of length $k$. Prove that


$W(k,2)=\Omega (2^{\frac{k}{2}})$.
7 replies
goodar2006
Sep 15, 2012
quantam13
2 hours ago
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Trivial Factoring MathCounts Question? 2025 MathCounts National Sprint Round #29
ilikemath247365   34
N 2 hours ago by Charizard_637
What is the value of the expression below?

$\frac{(1! + 2! + 3!)(2! + 3! + 4!)(3! + 4! + 5!)...(98! + 99! + 100!)}{(1! - 3(2!) + 3!)(2! - 3(3!) + 4!)(3! - 3(4!) + 5!)...(98! - 3(99!) + 100!)}$.
34 replies
ilikemath247365
Yesterday at 1:16 AM
Charizard_637
2 hours ago
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Maxi-inequality
giangtruong13   0
2 hours ago
Let $a,b,c >0$ and $a+b+c=2abc$. Find max: $$P= \sum_{cyc} \frac{a+2}{\sqrt{6(a^2+2)}}$$
0 replies
giangtruong13
2 hours ago
0 replies
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I cant find one problem
tanujkundu   9
N Apr 3, 2025 by vsarg
Does anybody know which problem is about when a number is a meteor and when a number is a shooting star?
9 replies
tanujkundu
Sep 17, 2024
vsarg
Apr 3, 2025
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I cant find one problem
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tanujkundu
8 posts
tanujkundu
#1 h  Sep 17, 2024, 3:00 AM
Y by
Does anybody know which problem is about when a number is a meteor and when a number is a shooting star?
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aidan0626
1963 posts
aidan0626
#2 h  Sep 17, 2024, 3:37 AM • 1 Y
Y by vsarg
Hi, this description is very vague and we probably can't help you unless you have more information on what the problem is.
What website did you find it on?
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aaaaaaaabbbb
148 posts
aaaaaaaabbbb
#3 h  Sep 17, 2024, 8:11 AM • 1 Y
Y by vsarg
Can you give more clue? Which contest is it?

The only question I found about shooting is this one AIME
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kamuii
232 posts
kamuii
#4 h  Sep 17, 2024, 8:54 PM • 1 Y
Y by vsarg
I saw one about shooting stars in intro to counting and prob
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cyberhacker
402 posts
cyberhacker
#5 h  Sep 17, 2024, 11:26 PM
Y by
this one?
Attachments:
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aritkr
1 post
aritkr
#6 h  Dec 10, 2024, 11:36 PM • 1 Y
Y by vsarg
tanujkundu wrote:
Does anybody know which problem is about when a number is a meteor and when a number is a shooting star?

check the number theory book
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GallopingUnicorn45
461 posts
GallopingUnicorn45
#7 h  Dec 12, 2024, 4:44 PM • 1 Y
Y by vsarg
It's in the C&P Intro book, that's the only one I know of.
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tanujkundu
8 posts
tanujkundu
#8 h  Apr 2, 2025, 7:30 PM • 1 Y
Y by vsarg
Thank you, everyone! I appreciate your help.
This post has been edited 1 time. Last edited by tanujkundu, Apr 2, 2025, 7:30 PM
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sadas123
1327 posts
sadas123
#9 h  Apr 2, 2025, 8:35 PM • 1 Y
Y by vsarg
tanujkundu wrote:
Thank you, everyone! I appreciate your help.

There is a problem like that in NT.
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vsarg
296 posts
vsarg
#10 h  Apr 3, 2025, 1:47 AM
Y by
I think thares a prowabiltyh quest leik thatt
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