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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:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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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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bracelets
pythagorazz   7
N 10 minutes ago by H1u2g4o4
Kat designs circular bead bracelets for kids. Each bracelet has 5 beads, all of which are either yellow or green. If beads of the same color are identical, how many distinct bracelets could Kat make?
7 replies
pythagorazz
Apr 14, 2025
H1u2g4o4
10 minutes ago
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hard problem
Cobedangiu   6
N 16 minutes ago by Jackson0423
Let $x,y,z>0$ and $xy+yz+zx=3$ : Prove that :
$\sum \ \frac{x}{y+z}\ge\sum \frac{1}{\sqrt{x+3}}$
6 replies
Cobedangiu
Apr 2, 2025
Jackson0423
16 minutes ago
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2016 Kmo Final round
Jackson0423   0
18 minutes ago
Source: 2016 FKMO P4
Let \(x,y,z\in\mathbb R\) with \(x^{2}+y^{2}+z^{2}=1\).
Find the maximum value of
\[ (x^{2}-yz)(y^{2}-zx)(z^{2}-xy). \]
0 replies
Jackson0423
18 minutes ago
0 replies
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Factor sums of integers
Aopamy   1
N 21 minutes ago by BR1F1SZ
Let $n$ be a positive integer. A positive integer $k$ is called a benefactor of $n$ if the positive divisors of $k$ can be partitioned into two sets $A$ and $B$ such that $n$ is equal to the sum of elements in $A$ minus the sum of the elements in $B$. Note that $A$ or $B$ could be empty, and that the sum of the elements of the empty set is $0$.

For example, $15$ is a benefactor of $18$ because $1+5+15-3=18$.

Show that every positive integer $n$ has at least $2023$ benefactors.
1 reply
Aopamy
Feb 23, 2023
BR1F1SZ
21 minutes ago
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Bogus Proof Marathon
pifinity   7609
N 25 minutes ago by e_is_2.71828
Hi!
I'd like to introduce the Bogus Proof Marathon.

In this marathon, simply post a bogus proof that is middle-school level and the next person will find the error. You don't have to post the real solution :P

Use classic Marathon format: 
[hide=P#]a1b2c3[/hide]
[hide=S#]a1b2c3[/hide]


Example posts:

P(x)
-----
S(x)
P(x+1)
-----
Let's go!! Just don't make it too hard!
7609 replies
pifinity
Mar 12, 2018
e_is_2.71828
25 minutes ago
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All prime factors under 8
qwedsazxc   23
N 37 minutes ago by Giant_PT
Source: 2023 KMO Final Round Day 2 Problem 4
Find all positive integers $n$ satisfying the following.
$$2^n-1 \text{ doesn't have a prime factor larger than } 7$$
23 replies
qwedsazxc
Mar 26, 2023
Giant_PT
37 minutes ago
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Interesting F.E
Jackson0423   14
N 37 minutes ago by Jackson0423
Show that there does not exist a function
\[ f : \mathbb{R}^+ \to \mathbb{R} \]satisfying the condition that for all \( x, y \in \mathbb{R}^+ \),
\[ f(x + y^2) \geq f(x) + y. \]

~Korea 2017 P7
14 replies
Jackson0423
Apr 18, 2025
Jackson0423
37 minutes ago
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Website to learn math
hawa   40
N 39 minutes ago by K1mchi_
Hi, I'm kinda curious what website do yall use to learn math, like i dont find any website thats fun to learn math
40 replies
hawa
Apr 9, 2025
K1mchi_
39 minutes ago
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2^x+3^x = yx^2
truongphatt2668   0
39 minutes ago
Prove that the following equation has infinite integer solutions:
$$2^x+3^x = yx^2$$
0 replies
truongphatt2668
39 minutes ago
0 replies
J
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1234th Post!
PikaPika999   144
N 42 minutes ago by K1mchi_
I hit my 1234th post! (I think I missed it, I'm kinda late, :oops_sign:)

But here's a puzzle for you all! Try to create the numbers 1 through 25 using the numbers 1, 2, 3, and 4! You are only allowed to use addition, subtraction, multiplication, division, and parenthesis. If you're post #1, try to make 1. If you're post #2, try to make 2. If you're post #3, try to make 3, and so on. If you're a post after 25, then I guess you can try to make numbers greater than 25 but you can use factorials, square roots, and that stuff. Have fun!

1: $(4-3)\cdot(2-1)$
144 replies
PikaPika999
Yesterday at 8:54 PM
K1mchi_
42 minutes ago
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Inequalities make a comeback
MS_Kekas   2
N an hour ago by ZeroHero
Source: Kyiv City MO 2025 Round 1, Problem 11.5
Determine the largest possible constant \( C \) such that for any positive real numbers \( x, y, z \), which are the sides of a triangle, the following inequality holds:
\[ \frac{xy}{x^2 + y^2 + xz} + \frac{yz}{y^2 + z^2 + yx} + \frac{zx}{z^2 + x^2 + zy} \geq C. \]
Proposed by Vadym Solomka
2 replies
MS_Kekas
Jan 20, 2025
ZeroHero
an hour ago
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Geometry Problem
Itoz   3
N an hour ago by Itoz
Source: Own
Given $\triangle ABC$. Let the perpendicular line from $A$ to $BC$ meets $BC,\odot(ABC)$ at points $S,K$, respectively, and the foot from $B$ to $AC$ is $L$. $\odot (AKL)$ intersects line $AB$ at $T(\neq A)$, $\odot(AST)$ intersects line $AC$ at $M(\neq A)$, and lines $TM,CK$ intersect at $N$.

Prove that $\odot(CNM)$ is tangent to $\odot (BST)$.
3 replies
Itoz
Apr 18, 2025
Itoz
an hour ago
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Nasty Floor Sum with Omega Function
Kezer   9
N an hour ago by lpieleanu
Source: Bulgaria 1989, Evan Chen's Summation Handout
Let $\Omega(n)$ denote the number of prime factors of $n$, counted with multiplicity. Evaluate \[ \sum_{n=1}^{1989} (-1)^{\Omega(n)}\left\lfloor \frac{1989}{n} \right \rfloor. \]
9 replies
Kezer
Jul 15, 2017
lpieleanu
an hour ago
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combinatorial geo question
SAAAAAAA_B   2
N 2 hours ago by R8kt
Kuba has two finite families $\mathcal{A}, \mathcal{B}$ of convex polygons (in the plane). It turns out that every point of the plane lies in the same number of elements of $\mathcal{A}$ as elements of $\mathcal{B}$. Prove that $|\mathcal{A}| = |\mathcal{B}|$.

\textit{Note:} We treat segments and points as degenerate convex polygons, and they can be elements of $\mathcal{A}$ or $\mathcal{B}$.
2 replies
SAAAAAAA_B
Apr 14, 2025
R8kt
2 hours ago
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State target p8 sol
EaZ_Shadow   116
N Apr 18, 2025 by derekwang2048
This solution was so educational! It helped me understand how to solve this problem in many ways I couldn't, and I feel so enlightened!
116 replies
EaZ_Shadow
Apr 6, 2025
derekwang2048
Apr 18, 2025
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State target p8 sol
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