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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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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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Easy inequality...
Sadigly   1
N an hour ago by lbh_qys
Source: Azerbaijan Senior NMO 2020
$x,y,z\in\mathbb{R^+}$. If $xyz=1$, then prove the following: $$\sum\frac{x^6+2}{x^3}\geq3(\frac{x}{y}+\frac{y}{z}+\frac{z}{x})$$
1 reply
Sadigly
Yesterday at 9:57 PM
lbh_qys
an hour ago
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Compilation of functions problems
Saucepan_man02   3
N an hour ago by Saucepan_man02
Could anyone post some handout/compilation of problems related to functions (difficulty similar to AIME/ARML/HMMT etc)?

Thanks..
3 replies
Saucepan_man02
May 7, 2025
Saucepan_man02
an hour ago
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PIE practice
Serengeti22   0
an hour ago
Does anybody know any good problems to practice PIE that range from mid-AMC10/12 level - early AIME level for pracitce.
0 replies
Serengeti22
an hour ago
0 replies
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people in the circle
Pomegranat   0
2 hours ago
Source: idk

Let $n \geq 5$ people be arranged in a circle, numbered clockwise from $1$ to $n$. These people are eliminated one by one in order, until only one person remains. The elimination follows this rule: among the remaining people, start counting clockwise from the person with the smallest number, and eliminate the $n$-th person in that count. Then, among the remaining people, start counting again from the person with the smallest number and eliminate the $n$-th person. Repeat this process until only one person remains. Let $W(n)$ denote the number of the last remaining person.

For example, when $n = 5$, people are eliminated in the following order: $5, 1, 3, 2$. Thus, $W(5) = 4$. It is known that $W(n) = n - 4$ under certain conditions. Prove that the necessary and sufficient condition for this is that both $n + 1$ and $n/2$ are prime numbers.
0 replies
Pomegranat
2 hours ago
0 replies
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ISI UGB 2025 P4
SomeonecoolLovesMaths   5
N 2 hours ago by mqoi_KOLA
Source: ISI UGB 2025 P4
Let $S^1 = \{ z \in \mathbb{C} \mid |z| =1 \}$ be the unit circle in the complex plane. Let $f \colon S^1 \longrightarrow S^2$ be the map given by $f(z) = z^2$. We define $f^{(1)} \colon = f$ and $f^{(k+1)} \colon = f \circ f^{(k)}$ for $k \geq 1$. The smallest positive integer $n$ such that $f^{(n)}(z) = z$ is called the period of $z$. Determine the total number of points in $S^1$ of period $2025$.
(Hint : $2025 = 3^4 \times 5^2$)
5 replies
SomeonecoolLovesMaths
Yesterday at 11:24 AM
mqoi_KOLA
2 hours ago
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hard inequality omg
tokitaohma   3
N 2 hours ago by tokitaohma
1. Given $a, b, c > 0$ and $abc=1$
Prove that: $ \sqrt{a^2+1} + \sqrt{b^2+1} + \sqrt{c^2+1} \leq \sqrt{2}(a+b+c) $

2. Given $a, b, c > 0$ and $a+b+c=1 $
Prove that: $ \dfrac{\sqrt{a^2+2ab}}{\sqrt{b^2+2c^2}} + \dfrac{\sqrt{b^2+2bc}}{\sqrt{c^2+2a^2}} + \dfrac{\sqrt{c^2+2ca}}{\sqrt{a^2+2b^2}} \geq \dfrac{1}{a^2+b^2+c^2} $
3 replies
+1 w
tokitaohma
Yesterday at 5:24 PM
tokitaohma
2 hours ago
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Divisibilty...
Sadigly   5
N 2 hours ago by COCBSGGCTG3
Source: Azerbaijan Junior NMO 2025 P2
Find all $4$ consecutive even numbers, such that the sum of their squares divides the square of their product.
5 replies
Sadigly
Saturday at 9:07 PM
COCBSGGCTG3
2 hours ago
J
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Diophantine involving cube
Sadigly   1
N 2 hours ago by mashumaro
Source: Azerbaijan Senior NMO 2020
$a;b;c;d\in\mathbb{Z^+}$. Solve the equation: $$2^{a!}+2^{b!}+2^{c!}=d^3$$
1 reply
Sadigly
Yesterday at 10:13 PM
mashumaro
2 hours ago
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Old hard problem
ItzsleepyXD   2
N 3 hours ago by ItzsleepyXD
Source: IDK
Let $ABC$ be a triangle and let $O$ be its circumcenter and $I$ its incenter.
Let $P$ be the radical center of its three mixtilinears and let $Q$ be the isogonal conjugate of $P$.
Let $G$ be the Gergonne point of the triangle $ABC$.
Prove that line $QG$ is parallel with line $OI$ .
2 replies
ItzsleepyXD
Apr 25, 2025
ItzsleepyXD
3 hours ago
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Square number
linkxink0603   5
N 3 hours ago by linkxink0603
Find m is positive interger such that m^4+3^m is square number
5 replies
linkxink0603
May 9, 2025
linkxink0603
3 hours ago
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The Return of Triangle Geometry
peace09   9
N 3 hours ago by mathfun07
Source: 2023 ISL A7
Let $N$ be a positive integer. Prove that there exist three permutations $a_1,\dots,a_N$, $b_1,\dots,b_N$, and $c_1,\dots,c_N$ of $1,\dots,N$ such that \[\left|\sqrt{a_k}+\sqrt{b_k}+\sqrt{c_k}-2\sqrt{N}\right|<2023\]for every $k=1,2,\dots,N$.
9 replies
peace09
Jul 17, 2024
mathfun07
3 hours ago
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Set Partition
Butterfly   0
3 hours ago
For the set of positive integers $\{1,2,…,n\}(n\ge 3)$, no matter how its elements are partitioned into two subsets, at least one of the subsets must contain three numbers $a,b,c$ ($a=b$ is allowed) such that $ab=c$. Find the minimal $n$.
0 replies
Butterfly
3 hours ago
0 replies
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Points Lying on its Cevian Triangle's Thomson Cubic
Feuerbach-Gergonne   1
N 4 hours ago by golue3120
Source: Own
Given $\triangle ABC$ and a point $P$, let $\triangle DEF$ be the cevian triangle of $P$ with respect to $\triangle ABC$. Let $H$ be the orthocenter of $\triangle ABC$, and denote the isotomic conjugate of $H, P$ with respect to $\triangle ABC$ by $X, Q$, respectively. Let the centroid of $\triangle DEF$ be $M$, and denote the isogonal conjugate of $P$ with respect to $\triangle DEF$ by $R$. Prove that
$$ P, Q, X \text{ are collinear} \iff P, R, M \text{ are collinear}. $$or in brief
$$ P \in \text{ K007 of } \triangle ABC \iff P \in \text{ K002 of } \triangle DEF. $$
1 reply
Feuerbach-Gergonne
Jul 19, 2024
golue3120
4 hours ago
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Functions
Entrepreneur   5
N 4 hours ago by RandomMathGuy500
Let $f(x)$ be a polynomial with integer coefficients such that $f(0)=2020$ and $f(a)=2021$ for some integer $a$. Prove that there exists no integer $b$ such that $f(b) = 2022$.
5 replies
Entrepreneur
Aug 18, 2023
RandomMathGuy500
4 hours ago
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hard number theory
eric201291   2
N Apr 18, 2025 by eric201291
Prove:There are no integers x, y, that y^2+9998587980=x^3.
2 replies
eric201291
Apr 16, 2025
eric201291
Apr 18, 2025
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hard number theory
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Reveal topic tags
number theory
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eric201291
208 posts
eric201291
#1 h  Apr 16, 2025, 2:17 PM
Y by
Prove:There are no integers x, y, that y^2+9998587980=x^3.
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Kempu33334
610 posts
Kempu33334
#2 h  Apr 17, 2025, 12:50 AM
Y by
This is a Mordell curve, however I don't know how to prove that this doesn't have any solutions. Perhaps such kind of modulo or manipulation (I can't find one)?
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eric201291
208 posts
eric201291
#3 h  Apr 18, 2025, 9:22 AM
Y by
Let me tell you sth:9998587980=2154^3+2154^2, and this thing is very important, so...
y^2+2154^2=x^3-2154^3, so by (-1/p) when p=4k+3 is -1, so done!
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