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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.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
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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
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
J
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law of log
Miranda2829   8
N a minute ago by jkim0656
5log (5²) + 8 ˡºᵍ₈4 =

is this answer 6?
8 replies
+1 w
Miranda2829
2 hours ago
jkim0656
a minute ago
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Inequalities
sqing   1
N 19 minutes ago by sqing
Let $ a,b,c $ be real numbers so that $ a+2b+3c=2 $ and $ 2ab+6bc+3ca =1. $ Show that
$$-\frac{1}{6} \leq ab-bc+ ca\leq \frac{1}{2}$$$$\frac{5-\sqrt{61}}{9} \leq a-b+c\leq \frac{5+\sqrt{61}}{9} $$
1 reply
1 viewing
sqing
Yesterday at 2:40 PM
sqing
19 minutes ago
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Integral solutions
KDS   4
N 34 minutes ago by Maximilian113
Source: Romania TST 1993
Prove that the equation $ (x+y)^n=x^m+y^m$ has a unique solution in integers with $ x>y>0$ and $ m,n>1$.
4 replies
KDS
Jul 12, 2009
Maximilian113
34 minutes ago
J
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F=(F^3+F^3)/9-2F^3
Yiyj1   0
44 minutes ago
Source: 101 Algebra Problems for the AMSP
Define the Fibonacci sequence $F_n$ as $$F_1=F_2=1, F_{n+1}+F_n=F_{n-1}$$fir $n \in \mathbb{N}$. Prove that $$F_{2n}=\dfrac{F_{2n+2}^3+F_{2n-2}^3}{9}-2F_{2n}^3$$for all $n \ge 2$.
0 replies
Yiyj1
44 minutes ago
0 replies
J
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4 lines concurrent
Zavyk09   2
N an hour ago by aidenkim119
Source: Homework
Let $ABC$ be triangle with circumcenter $(O)$ and orthocenter $H$. $BH, CH$ intersect $(O)$ again at $K, L$ respectively. Lines through $H$ parallel to $AB, AC$ intersects $AC, AB$ at $E, F$ respectively. Point $D$ such that $HKDL$ is a parallelogram. Prove that lines $KE, LF$ and $AD$ are concurrent at a point on $OH$.
2 replies
Zavyk09
Yesterday at 11:51 AM
aidenkim119
an hour ago
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Inequality => square
Rushil   13
N an hour ago by mqoi_KOLA
Source: INMO 1998 Problem 4
Suppose $ABCD$ is a cyclic quadrilateral inscribed in a circle of radius one unit. If $AB \cdot BC \cdot CD \cdot DA \geq 4$, prove that $ABCD$ is a square.
13 replies
Rushil
Oct 7, 2005
mqoi_KOLA
an hour ago
J
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Circle and square
Marrelia   0
an hour ago
Given a circle with center $O$, and square $ABCD$. Point $A$ and $B$ are on the circle, and $CD$ is tangent to the circle at point $E$. Let $M$ represent the midpoint of $AD$ and $F$ represent the intersection between $AD$ and circle. Prove that $MF = FD$.
0 replies
Marrelia
an hour ago
0 replies
J
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where a, b, c are positive real numbers
eyesofgod1930   2
N an hour ago by sqing
where $a, b, c$ are positive real numbers.Prove that
$\frac{4}{\sqrt{a^{2}+b^{2}+c^{2}+4}}-\frac{9}{\sqrt{(a+b)\sqrt{(a+2c)(b+2c)}}}\leq \frac{5}{8}$
2 replies
eyesofgod1930
Jun 8, 2020
sqing
an hour ago
J
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Hard number theory
td12345   3
N an hour ago by mathprodigy2011
Let $q$ be a prime number. Define the set
\[ M_q = \left\{ x \in \mathbb{Z}^* \,\middle|\, \sqrt{x^2 + 2q^{2025} x} \in \mathbb{Q} \right\}. \]
Find the number of elements of \(M_2 \cup M_{2027}\).
3 replies
td12345
4 hours ago
mathprodigy2011
an hour ago
J
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NT function debut
AshAuktober   4
N an hour ago by AshAuktober
Source: 2025 Nepal Practice TST 3 P2 of 3; Own
Let $f$ be a function taking in positive integers and outputting nonnegative integers, defined as follows:
$f(m)$ is the number of positive integers $n$ with $n \le m$ such that the equation $$an + bm = m^2 + n^2 + 1$$has an integer solution $(a, b)$.
Find all positive integers $x$ such that$f(x) \ne 0$ and $$f(f(x)) = f(x) - 1.$$(Adit Aggarwal, India.)
4 replies
AshAuktober
Yesterday at 3:53 PM
AshAuktober
an hour ago
J
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Inspired by 2025 Nepal
sqing   1
N 2 hours ago by sqing
Source: Own
Let $ a, b, c $ be positive reals such that $ a+b +c+abc = 4 $. Prove that
$$ \frac{1}{a+1} + \frac{1}{b+1} + \frac{1}{c+ 1}\leq\frac{3}{2}(2 - abc) $$$$ \frac{1}{ab+1} + \frac{1}{bc+1} + \frac{1}{ca + 1}\leq\frac{3}{2}(2 - abc) $$
1 reply
sqing
2 hours ago
sqing
2 hours ago
J
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Inspired by Ruji2018252
sqing   0
2 hours ago
Source: Own
Let $ a,b,c $ be reals such that $ a^2+b^2+c^2-2a-4b-4c=7. $ Prove that
$$ -4\leq 2a+b+2c\leq 20$$$$5-4\sqrt 3\leq a+b+c\leq 5+4\sqrt 3$$$$ 11-4\sqrt {14}\leq a+2b+3c\leq 11+4\sqrt {14}$$
0 replies
sqing
2 hours ago
0 replies
J
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Isos Trap
MithsApprentice   38
N 2 hours ago by eg4334
Source: USAMO 1999 Problem 6
Let $ABCD$ be an isosceles trapezoid with $AB \parallel CD$. The inscribed circle $\omega$ of triangle $BCD$ meets $CD$ at $E$. Let $F$ be a point on the (internal) angle bisector of $\angle DAC$ such that $EF \perp CD$. Let the circumscribed circle of triangle $ACF$ meet line $CD$ at $C$ and $G$. Prove that the triangle $AFG$ is isosceles.
38 replies
MithsApprentice
Oct 3, 2005
eg4334
2 hours ago
J
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Funny function that there isn't exist
ItzsleepyXD   0
2 hours ago
Source: Own, Modified from old problem
Determine all functions $f\colon\mathbb{Z}_{>0}\to\mathbb{Z}_{>0}$ such that, for all positive integers $m$ and $n$,
$$ m^{\phi(n)}+n^{\phi(m)} \mid f(m)^n + f(n)^m$$
0 replies
ItzsleepyXD
2 hours ago
0 replies
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J
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Probability
Ecrin_eren   2
N Tuesday at 1:29 PM by Ecrin_eren
In a board, James randomly writes A , B or C in each cell. What is the probability that, for every row and every column, the number of A 's modulo 3 is equal to the number of B's modulo 3?

2 replies
Ecrin_eren
Apr 3, 2025
Ecrin_eren
Tuesday at 1:29 PM
J
Probability
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Reveal topic tags
combinatorics
probability
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Ecrin_eren
42 posts
Ecrin_eren
#1 h  Apr 3, 2025, 11:21 AM
Y by
In a board, James randomly writes A , B or C in each cell. What is the probability that, for every row and every column, the number of A 's modulo 3 is equal to the number of B's modulo 3?
Z K Y
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Ecrin_eren
42 posts
Ecrin_eren
#2 h  Apr 4, 2025, 1:38 PM
Y by
Bump bump
Z K Y
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Ecrin_eren
42 posts
Ecrin_eren
#3 h  Tuesday at 1:29 PM
Y by
Bump....
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N Quick Reply
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