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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
1 viewing
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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fractions question
kjhgyuio   2
N 41 minutes ago by Filipjack

........
2 replies
kjhgyuio
an hour ago
Filipjack
41 minutes ago
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A hard cyclic one
Sondtmath0x1   2
N an hour ago by Sondtmath0x1
Source: unknown
Help me please!
2 replies
Sondtmath0x1
4 hours ago
Sondtmath0x1
an hour ago
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Circle geometry
nAalniaOMliO   1
N an hour ago by RaeT
Source: Belarusian MO 2021
A convex quadrilateral $ABCD$ is given. $\omega_1$ is a circle with diameter $BC$, $\omega_2$ is a circle with diameter $AD$. $AC$ meets $\omega_1$ and $\omega_2$ for the second time at $B_1$ and $D_1$. $BD$ meets $\omega_1$ and $\omega_2$ for the second time at $C_1$ and $A_1$. $AA_1$ meets $DD_1$ at $X$, $BB_1$ meets $CC_1$ at $Y$. $\omega_1$ intersects $\omega_2$ at $P$ and $Q$. $XY$ meets $PQ$ at $N$.
Prove that $XN=NY$.
1 reply
nAalniaOMliO
Apr 16, 2024
RaeT
an hour ago
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Find < BAC given MB = OI
math163   7
N 2 hours ago by Nari_Tom
Source: Baltic Way 2017 Problem 13
Let $ABC$ be a triangle in which $\angle ABC = 60^{\circ}$. Let $I$ and $O$ be the incentre and circumcentre of $ABC$, respectively. Let $M$ be the midpoint of the arc $BC$ of the circumcircle of $ABC$, which does not contain the point $A$. Determine $\angle BAC$ given that $MB = OI$.
7 replies
math163
Nov 11, 2017
Nari_Tom
2 hours ago
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All Russian Olympiad Day 1 P4
Davrbek   13
N 2 hours ago by bin_sherlo
Source: Grade 11 P4
On the sides $AB$ and $AC$ of the triangle $ABC$, the points $P$ and $Q$ are chosen, respectively, so that $PQ\parallel BC$. Segments $BQ$ and $CP$ intersect at point $O$. Point $A'$ is symmetric to point $A$ relative to line $BC$. The segment $A'O$ intersects the circumcircle $w$ of the triangle $APQ$ at the point $S$. Prove that circumcircle of $BSC$ is tangent to the circle $w$.
13 replies
Davrbek
Apr 28, 2018
bin_sherlo
2 hours ago
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Geometry
youochange   8
N 2 hours ago by RANDOM__USER
m:}
Let $\triangle ABC$ be a triangle inscribed in a circle, where the tangents to the circle at points $B$ and $C$ intersect at the point $P$. Let $M$ be a point on the arc $AC$ (not containing $B$) such that $M \neq A$ and $M \neq C$. Let the lines $BC$ and $AM$ intersect at point $K$. Let $P'$ be the reflection of $P$ with respect to the line $AM$. The lines $AP'$ and $PM$ intersect at point $Q$, and $PM$ intersects the circumcircle of $\triangle ABC$ again at point $N$.

Prove that the point $Q$ lies on the circumcircle of $\triangle ANK$.
8 replies
youochange
Yesterday at 11:27 AM
RANDOM__USER
2 hours ago
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Geometry
IstekOlympiadTeam   27
N 2 hours ago by SimplisticFormulas
Source: All Russian Grade 9 Day 2 P 3
An acute-angled $ABC \ (AB<AC)$ is inscribed into a circle $\omega$. Let $M$ be the centroid of $ABC$, and let $AH$ be an altitude of this triangle. A ray $MH$ meets $\omega$ at $A'$. Prove that the circumcircle of the triangle $A'HB$ is tangent to $AB$. (A.I. Golovanov , A.Yakubov)
27 replies
IstekOlympiadTeam
Dec 12, 2015
SimplisticFormulas
2 hours ago
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Incenter and concurrency
jenishmalla   3
N 2 hours ago by Captainscrubz
Source: 2025 Nepal ptst p3 of 4
Let the incircle of $\triangle ABC$ touch sides $BC$, $CA$, and $AB$ at points $D$, $E$, and $F$, respectively. Let $D'$ be the diametrically opposite point of $D$ with respect to the incircle. Let lines $AD'$ and $AD$ intersect the incircle again at $X$ and $Y$, respectively. Prove that the lines $DX$, $D'Y$, and $EF$ are concurrent, i.e., the lines intersect at the same point.

(Kritesh Dhakal, Nepal)
3 replies
jenishmalla
Mar 15, 2025
Captainscrubz
2 hours ago
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Number Theory Chain!
JetFire008   1
N 3 hours ago by whwlqkd
I will post a question and someone has to answer it. Then they have to post a question and someone else will answer it and so on. We can only post questions related to Number Theory and each problem should be more difficult than the previous. Let's start!

Question 1
1 reply
JetFire008
3 hours ago
whwlqkd
3 hours ago
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Collinearity with orthocenter
math163   6
N 3 hours ago by Nari_Tom
Source: Baltic Way 2017 Problem 11
Let $H$ and $I$ be the orthocenter and incenter, respectively, of an acute-angled triangle $ABC$. The circumcircle of the triangle $BCI$ intersects the segment $AB$ at the point $P$ different from $B$. Let $K$ be the projection of $H$ onto $AI$ and $Q$ the reflection of $P$ in $K$. Show that $B$, $H$ and $Q$ are collinear.

Proposed by Mads Christensen, Denmark
6 replies
math163
Nov 11, 2017
Nari_Tom
3 hours ago
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inequalities 070425
pennypc123456789   5
N 4 hours ago by Sadigly
Let $a,b,c$ be positive real numbers . Prove that :
$$\dfrac{2ab}{a^2+b^2} + \dfrac{2bc}{b^2+c^2} + \dfrac{2ac}{a^2+c^2} \ge \dfrac{24abc}{(a+b)(b+c)(a+c)} $$
5 replies
1 viewing
pennypc123456789
6 hours ago
Sadigly
4 hours ago
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inequalities such a hard problem
mannothot11   10
N 5 hours ago by sqing
for all real x y z and x^2 + y^2 +z^2 = 1
Prove that xy + y^2 +2xz≤ (√3 +1)/2

ps: forgive me because i don know how to edit this
10 replies
mannothot11
Jan 16, 2018
sqing
5 hours ago
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Inequalities
sqing   6
N 5 hours ago by sqing
Let $a,b$ be real numbers such that $ a^2+b^2+a^3 +b^3=4 . $ Prove that
$$a+b \leq 2$$Let $a,b$ be real numbers such that $a+b + a^2+b^2+a^3 +b^3=6 . $ Prove that
$$a+b \leq 2$$
6 replies
sqing
Saturday at 1:10 PM
sqing
5 hours ago
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Congruence
Ecrin_eren   3
N Today at 3:39 AM by lbh_qys
Find the number of integer pairs (x, y) satisfying the congruence equation:

3y² + 3x²y + y³ ≡ 3x² (mod 41)

for 0 ≤ x, y < 41.

3 replies
Ecrin_eren
Apr 3, 2025
lbh_qys
Today at 3:39 AM
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rectangles of = areas and perimeters (2012 Polish JMO R1 p3)
parmenides51   1
N Apr 2, 2021 by Vanew
There are two rectangles with equal areas and equal perimeters. Prove length og the diagonals of both rectangles are also equal.
1 reply
parmenides51
Apr 2, 2021
Vanew
Apr 2, 2021
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rectangles of = areas and perimeters (2012 Polish JMO R1 p3)
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Reveal topic tags
geometry
rectangle
perimeter
equal areas
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parmenides51
30630 posts
parmenides51
#1 h  Apr 2, 2021, 7:31 AM
Y by
There are two rectangles with equal areas and equal perimeters. Prove length og the diagonals of both rectangles are also equal.
Z K Y
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Vanew
18 posts
Vanew
#2 h  Apr 2, 2021, 9:01 AM
Y by
Suppose the side lengths of two rectangles are $a, b$ and $c, d$, thus we have $ab=cd$ and $a+b=c+d$, so it's obvious that $a^2+b^2=c^2+d^2$.
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