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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
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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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H not needed
dchenmathcounts   45
N 7 minutes ago by EpicBird08
Source: USEMO 2019/1
Let $ABCD$ be a cyclic quadrilateral. A circle centered at $O$ passes through $B$ and $D$ and meets lines $BA$ and $BC$ again at points $E$ and $F$ (distinct from $A,B,C$). Let $H$ denote the orthocenter of triangle $DEF.$ Prove that if lines $AC,$ $DO,$ $EF$ are concurrent, then triangle $ABC$ and $EHF$ are similar.

Robin Son
45 replies
dchenmathcounts
May 23, 2020
EpicBird08
7 minutes ago
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Functional Equation
AnhQuang_67   1
N 29 minutes ago by maromex
Find all functions $f: \mathbb{R} \to \mathbb{R}$ satisfying $$2\cdot f\Big(\dfrac{-xy}{2}+f(x+y)\Big)=xf(y)+y(x), \forall x, y \in \mathbb{R} $$











1 reply
AnhQuang_67
38 minutes ago
maromex
29 minutes ago
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Problem 1
blug   4
N 29 minutes ago by grupyorum
Source: Polish Math Olympiad 2025 Finals P1
Find all $(a, b, c, d)\in \mathbb{R}$ satisfying
\[\begin{aligned} \begin{cases} a+b+c+d=0,\\ a^2+b^2+c^2+d^2=12,\\ abcd=-3.\\ \end{cases} \end{aligned}\]
4 replies
blug
6 hours ago
grupyorum
29 minutes ago
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A board with crosses that we color
nAalniaOMliO   3
N an hour ago by nAalniaOMliO
Source: Belarusian National Olympiad 2025
In some cells of the table $2025 \times 2025$ crosses are placed. A set of 2025 cells we will call balanced if no two of them are in the same row or column. It is known that any balanced set has at least $k$ crosses.
Find the minimal $k$ for which it is always possible to color crosses in two colors such that any balanced set has crosses of both colors.
3 replies
nAalniaOMliO
Mar 28, 2025
nAalniaOMliO
an hour ago
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April Fools Geometry
awesomeming327.   6
N an hour ago by GreekIdiot
Let $ABC$ be an acute triangle with $AB<AC$, and let $D$ be the projection from $A$ onto $BC$. Let $E$ be a point on the extension of $AD$ past $D$ such that $\angle BAC+\angle BEC=90^\circ$. Let $L$ be on the perpendicular bisector of $AE$ such that $L$ and $C$ are on the same side of $AE$ and
\[\frac12\angle ALE=1.4\angle ABE+3.4\angle ACE-558^\circ\]Let the reflection of $D$ across $AB$ and $AC$ be $W$ and $Y$, respectively. Let $X\in AW$ and $Z\in AY$ such that $\angle XBE=\angle ZCE=90^\circ$. Let $EX$ and $EZ$ intersect the circumcircles of $EBD$ and $ECD$ at $J$ and $K$, respectively. Let $LB$ and $LC$ intersect $WJ$ and $YK$ at $P$ and $Q$. Let $PQ$ intersect $BC$ at $F$. Prove that $FB/FC=DB/DC$.
6 replies
awesomeming327.
Apr 1, 2025
GreekIdiot
an hour ago
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Functional equations
hanzo.ei   14
N an hour ago by jasperE3
Source: Greekldiot
Find all $f: \mathbb R_+ \rightarrow \mathbb R_+$ such that $f(xf(y)+f(x))=yf(x+yf(x)) \: \forall \: x,y \in \mathbb R_+$
14 replies
hanzo.ei
Mar 29, 2025
jasperE3
an hour ago
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Problem 1
SlovEcience   2
N an hour ago by Raven_of_the_old
Prove that
\[ C(p-1, k-1) \equiv (-1)^{k-1} \pmod{p} \]for \( 1 \leq k \leq p-1 \), where \( C(n, m) \) is the binomial coefficient \( n \) choose \( m \).
2 replies
SlovEcience
2 hours ago
Raven_of_the_old
an hour ago
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Conditional maximum
giangtruong13   1
N an hour ago by giangtruong13
Source: Specialized Math
Let $a,b$ satisfy that: $1 \leq a \leq2$ and $1 \leq b \leq 2$. Find the maximum: $$A=(a+b^2+\frac{4}{a^2}+\frac{2}{b})(b+a^2+\frac{4}{b^2}+\frac{2}{a})$$
1 reply
1 viewing
giangtruong13
Mar 22, 2025
giangtruong13
an hour ago
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four variables inequality
JK1603JK   0
an hour ago
Source: unknown?
Prove that $$27(a^4+b^4+c^4+d^4)+148abcd\ge (a+b+c+d)^4,\ \ \forall a,b,c,d\ge 0.$$
0 replies
JK1603JK
an hour ago
0 replies
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a hard geometry problen
Tuguldur   0
2 hours ago
Let $ABCD$ be a convex quadrilateral. Suppose that the circles with diameters $AB$ and $CD$ intersect at points $X$ and $Y$. Let $P=AC\cap BD$ and $Q=AD\cap BC$. Prove that the points $P$, $Q$, $X$ and $Y$ are concyclic.
( $AB$ and $CD$ are not the diagnols)
0 replies
Tuguldur
2 hours ago
0 replies
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Problem 2
SlovEcience   0
2 hours ago
Let \( a, n \) be positive integers and \( p \) be an odd prime such that:
\[ a^p \equiv 1 \pmod{p^n}. \]Prove that:
\[ a \equiv 1 \pmod{p^{n-1}}. \]
0 replies
SlovEcience
2 hours ago
0 replies
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Regarding Maaths olympiad prepration
omega2007   1
N 2 hours ago by GreekIdiot
<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
2 hours ago
GreekIdiot
2 hours ago
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Induction
Mathlover_1   2
N 2 hours ago by GreekIdiot
Hello, can you share links of same interesting induction problems in algebra
2 replies
Mathlover_1
Mar 24, 2025
GreekIdiot
2 hours ago
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n-gon function
ehsan2004   10
N 2 hours ago by Zany9998
Source: Romanian IMO Team Selection Test TST 1996, problem 1
Let $ f: \mathbb{R}^2 \rightarrow \mathbb{R} $ be a function such that for every regular $ n $-gon $ A_1A_2 \ldots A_n $ we have $ f(A_1)+f(A_2)+\cdots +f(A_n)=0 $. Prove that $ f(x)=0 $ for all reals $ x $.
10 replies
ehsan2004
Sep 13, 2005
Zany9998
2 hours ago
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Ratio of projections of a tetrahedron on two planes.
Goutham   0
Mar 17, 2011
Prove that for any tetrahedron in space, it is possible to find two perpendicular planes such that ratio between the projections of the tetrahedron on the two planes lies in the interval $[\frac{1}{\sqrt{2}}, \sqrt{2}].$
0 replies
Goutham
Mar 17, 2011
0 replies
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Ratio of projections of a tetrahedron on two planes.
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Goutham
3130 posts
Goutham
#1 h  Mar 17, 2011, 5:45 PM • 2 Y
Y by Adventure10, Mango247
Prove that for any tetrahedron in space, it is possible to find two perpendicular planes such that ratio between the projections of the tetrahedron on the two planes lies in the interval $[\frac{1}{\sqrt{2}}, \sqrt{2}].$
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