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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 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
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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
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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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KSEA NMSC Mock Contest Group B (Last Problem)
Shiyul   5
N 2 hours ago by Shiyul
Let $a_n$ be a sequence defined by $a_n = a^2 + 1$. Then the product of four consecutive terms in $a_n$ can be written as the product of two terms in $a_n$. Find $p + q$ if $(a_(11))(a_(12))(a_(13))(a_(14)) = (a_p)(a_q)$.
5 replies
Shiyul
Yesterday at 3:09 PM
Shiyul
2 hours ago
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Distance vs time swimming problem
smalkaram_3549   0
2 hours ago
How should I approach a problem where we deal with velocities becoming negative and stuff. I know that they both travel 3 Lengths of the pool before meeting a second time.
0 replies
smalkaram_3549
2 hours ago
0 replies
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IMO ShortList 1998, algebra problem 1
orl   37
N 2 hours ago by Marcus_Zhang
Source: IMO ShortList 1998, algebra problem 1
Let $a_{1},a_{2},\ldots ,a_{n}$ be positive real numbers such that $a_{1}+a_{2}+\cdots +a_{n}<1$. Prove that

\[ \frac{a_{1} a_{2} \cdots a_{n} \left[ 1 - (a_{1} + a_{2} + \cdots + a_{n}) \right] }{(a_{1} + a_{2} + \cdots + a_{n})( 1 - a_{1})(1 - a_{2}) \cdots (1 - a_{n})} \leq \frac{1}{ n^{n+1}}. \]
37 replies
orl
Oct 22, 2004
Marcus_Zhang
2 hours ago
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Regarding IMO prepartion
omega2007   1
N 2 hours ago by omega2007
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compilled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your prespective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.
1 reply
omega2007
Yesterday at 3:14 PM
omega2007
2 hours ago
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Integer Coefficient Polynomial with order
MNJ2357   9
N 2 hours ago by v_Enhance
Source: 2019 Korea Winter Program Practice Test 1 Problem 3
Find all polynomials $P(x)$ with integer coefficients such that for all positive number $n$ and prime $p$ satisfying $p\nmid nP(n)$, we have $ord_p(n)\ge ord_p(P(n))$.
9 replies
MNJ2357
Jan 12, 2019
v_Enhance
2 hours ago
J
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Regarding Maaths olympiad prepration
omega2007   2
N 2 hours ago by omega2007
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compiled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your perspective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.
2 replies
omega2007
Yesterday at 3:13 PM
omega2007
2 hours ago
J
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School Math Problem
math_cool123   6
N 2 hours ago by anduran
Find all ordered pairs of nonzero integers $(a, b)$ that satisfy $$(a^2+b)(a+b^2)=(a-b)^3.$$
6 replies
math_cool123
Apr 2, 2025
anduran
2 hours ago
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Inspired by bamboozled
sqing   0
2 hours ago
Source: Own
Let $ a,b,c $ be reals such that $(a^2+1)(b^2+1)(c^2+1) = 27. $Prove that $$1-3\sqrt 3\leq ab + bc + ca\leq 6$$
0 replies
sqing
2 hours ago
0 replies
J
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Range of ab + bc + ca
bamboozled   1
N 3 hours ago by sqing
Let $(a^2+1)(b^2+1)(c^2+1) = 9$, where $a, b, c \in R$, then the number of integers in the range of $ab + bc + ca$ is __
1 reply
bamboozled
3 hours ago
sqing
3 hours ago
J
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Functional Equation
AnhQuang_67   4
N 3 hours ago by AnhQuang_67
Find all functions $f: \mathbb{R} \to \mathbb{R}$ satisfying $$2\cdot f\Big(\dfrac{-xy}{2}+f(x+y)\Big)=xf(y)+yf(x), \forall x, y \in \mathbb{R} $$
4 replies
AnhQuang_67
Yesterday at 4:50 PM
AnhQuang_67
3 hours ago
J
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Inradius and ex-radii
bamboozled   0
3 hours ago
Let $ABC$ be a triangle and $r, r_1, r_2, r_3$ denote its inradius and ex-radii opposite to the vertices $A, B, C$ respectively. If $a> r_1, b > r_2$ and $c > r_3$, then which of the following is/are true?
(A) $\angle{B}$ is obtuse
(B) $\angle{A}$ is acute
(C) $3r > s$, where $s$ is semi perimeter
(D) $3r < s$, where $s$ is semi perimeter
0 replies
bamboozled
3 hours ago
0 replies
J
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Inspired by giangtruong13
sqing   1
N 3 hours ago by sqing
Source: Own
Let $ a,b\in[\frac{1}{2},1] $. Prove that$$ 64\leq (a+b^2+\frac{4}{a^2}+\frac{2}{b})(b+a^2+\frac{4}{b^2}+\frac{2}{a})\leq\frac{6889}{16} $$Let $ a,b\in[\frac{1}{2},2] $. Prove that$$ 8(3+2\sqrt 2)\leq (a+b^2+\frac{4}{a^2}+\frac{2}{b})(b+a^2+\frac{4}{b^2}+\frac{2}{a})\leq\frac{6889}{16} $$
1 reply
sqing
3 hours ago
sqing
3 hours ago
J
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Conditional maximum
giangtruong13   2
N 3 hours ago by sqing
Source: Specialized Math
Let $a,b$ satisfy that: $1 \leq a \leq2$ and $1 \leq b \leq 2$. Find the maximum: $$A=(a+b^2+\frac{4}{a^2}+\frac{2}{b})(b+a^2+\frac{4}{b^2}+\frac{2}{a})$$
2 replies
giangtruong13
Mar 22, 2025
sqing
3 hours ago
J
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Inspired by JK1603JK
sqing   16
N 3 hours ago by sqing
Source: Own
Let $ a,b,c\geq 0 $ and $ab+bc+ca=1.$ Prove that$$\frac{abc-2}{abc-1}\ge \frac{4(a^2b+b^2c+c^2a)}{a^3b+b^3c+c^3a+1} $$
16 replies
sqing
Yesterday at 3:31 AM
sqing
3 hours ago
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distances from vertices of square (2018 Adygea Teachers' Geometry Olympiad p1)
parmenides51   2
N Jun 22, 2020 by stacy2020
Can the distances from a certain point on the plane to the vertices of a certain square be equal to $1, 4, 7$, and $8$ ?
2 replies
parmenides51
Jun 22, 2020
stacy2020
Jun 22, 2020
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distances from vertices of square (2018 Adygea Teachers' Geometry Olympiad p1)
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Reveal topic tags
geometry
square
distance
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parmenides51
30629 posts
parmenides51
#1 h  Jun 22, 2020, 7:21 PM
Y by
Can the distances from a certain point on the plane to the vertices of a certain square be equal to $1, 4, 7$, and $8$ ?
This post has been edited 1 time. Last edited by parmenides51, Jun 22, 2020, 7:22 PM
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Unidentifiable
193 posts
Unidentifiable
#2 h  Jun 22, 2020, 7:53 PM
Y by
I think it can
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stacy2020
142 posts
stacy2020
#3 h  Jun 22, 2020, 8:48 PM • 3 Y
Y by Mango247, Mango247, Mango247
$1^2+8^2=4^2+7^2=65$, so it is possible for a rectangle.
However, the side of a square must be in the range of $(3,5)$ and $(6,8)$, which is impossible.
This post has been edited 1 time. Last edited by stacy2020, Jun 22, 2020, 9:30 PM
Reason: correction
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