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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. 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 upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 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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4th grader qual JMO
HCM2001   48
N 17 minutes ago by nitride
i mean.. whattttt??? just found out about this.. is he on aops? (i'm sure he is) where are you orz lol..
https://www.mathschool.com/blog/results/celebrating-success-douglas-zhang-is-rsm-s-youngest-usajmo-qualifier
48 replies
HCM2001
May 22, 2025
nitride
17 minutes ago
J
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Wordy Geometry in Taiwan TST
ckliao914   9
N an hour ago by Scilyse
Source: 2023 Taiwan TST Round 3 Mock Exam 6
Given triangle $ABC$ with $A$-excenter $I_A$, the foot of the perpendicular from $I_A$ to $BC$ is $D$. Let the midpoint of segment $I_AD$ be $M$, $T$ lies on arc $BC$(not containing $A$) satisfying $\angle BAT=\angle DAC$, $I_AT$ intersects the circumcircle of $ABC$ at $S\neq T$. If $SM$ and $BC$ intersect at $X$, the perpendicular bisector of $AD$ intersects $AC,AB$ at $Y,Z$ respectively, prove that $AX,BY,CZ$ are concurrent.
9 replies
ckliao914
Apr 29, 2023
Scilyse
an hour ago
J
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Factorial Divisibility
Aryan-23   47
N an hour ago by ezpotd
Source: IMO SL 2022 N2
Find all positive integers $n>2$ such that
$$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$
47 replies
Aryan-23
Jul 9, 2023
ezpotd
an hour ago
J
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2-var inequality
sqing   3
N an hour ago by sqing
Source: Own
Let $ a,b> 0 ,a^3+ab+b^3=3.$ Prove that
$$ (a+b)(a+1)(b+1) \leq 8$$$$ (a^2+b^2)(a+1)(b+1) \leq 8$$Let $ a,b> 0 ,a^3+ab(a+b)+b^3=3.$ Prove that
$$ (a+b)(a+1)(b+1) \leq \frac{3}{2}+\sqrt[3]{6}+\sqrt[3]{36}$$
3 replies
sqing
2 hours ago
sqing
an hour ago
J
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Infinite number of sets with an intersection property
Drytime   8
N 2 hours ago by math90
Source: Romania TST 2013 Test 2 Problem 4
Let $k$ be a positive integer larger than $1$. Build an infinite set $\mathcal{A}$ of subsets of $\mathbb{N}$ having the following properties:

(a) any $k$ distinct sets of $\mathcal{A}$ have exactly one common element;
(b) any $k+1$ distinct sets of $\mathcal{A}$ have void intersection.
8 replies
Drytime
Apr 26, 2013
math90
2 hours ago
J
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Factorials divide
va2010   37
N 2 hours ago by ND_
Source: 2015 ISL N2
Let $a$ and $b$ be positive integers such that $a! + b!$ divides $a!b!$. Prove that $3a \ge 2b + 2$.
37 replies
va2010
Jul 7, 2016
ND_
2 hours ago
J
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IMO Shortlist 2011, Number Theory 2
orl   24
N 2 hours ago by ezpotd
Source: IMO Shortlist 2011, Number Theory 2
Consider a polynomial $P(x) = \prod^9_{j=1}(x+d_j),$ where $d_1, d_2, \ldots d_9$ are nine distinct integers. Prove that there exists an integer $N,$ such that for all integers $x \geq N$ the number $P(x)$ is divisible by a prime number greater than 20.

Proposed by Luxembourg
24 replies
orl
Jul 11, 2012
ezpotd
2 hours ago
J
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Inequality in triangle
Nguyenhuyen_AG   3
N 2 hours ago by Nguyenhuyen_AG
Let $a,b,c$ be the lengths of the sides of a triangle. Prove that
\[\frac{1}{(a-4b)^2}+\frac{1}{(b-4c)^2}+\frac{1}{(c-4a)^2} \geqslant \frac{1}{ab+bc+ca}.\]
3 replies
Nguyenhuyen_AG
Today at 6:17 AM
Nguyenhuyen_AG
2 hours ago
J
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Problem 1
randomusername   73
N 3 hours ago by ND_
Source: IMO 2015, Problem 1
We say that a finite set $\mathcal{S}$ of points in the plane is balanced if, for any two different points $A$ and $B$ in $\mathcal{S}$, there is a point $C$ in $\mathcal{S}$ such that $AC=BC$. We say that $\mathcal{S}$ is centre-free if for any three different points $A$, $B$ and $C$ in $\mathcal{S}$, there is no points $P$ in $\mathcal{S}$ such that $PA=PB=PC$.

(a) Show that for all integers $n\ge 3$, there exists a balanced set consisting of $n$ points.

(b) Determine all integers $n\ge 3$ for which there exists a balanced centre-free set consisting of $n$ points.

Proposed by Netherlands
73 replies
randomusername
Jul 10, 2015
ND_
3 hours ago
J
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x is rational implies y is rational
pohoatza   44
N 3 hours ago by ezpotd
Source: IMO Shortlist 2006, N2, VAIMO 2007, Problem 6
For $ x \in (0, 1)$ let $ y \in (0, 1)$ be the number whose $ n$-th digit after the decimal point is the $ 2^{n}$-th digit after the decimal point of $ x$. Show that if $ x$ is rational then so is $ y$.

Proposed by J.P. Grossman, Canada
44 replies
pohoatza
Jun 28, 2007
ezpotd
3 hours ago
J
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Multiplicative function
Tales   37
N 3 hours ago by ezpotd
Source: IMO Shortlist 2004, number theory problem 2
The function $f$ from the set $\mathbb{N}$ of positive integers into itself is defined by the equality \[f(n)=\sum_{k=1}^{n} \gcd(k,n),\qquad n\in \mathbb{N}.\]
a) Prove that $f(mn)=f(m)f(n)$ for every two relatively prime ${m,n\in\mathbb{N}}$.

b) Prove that for each $a\in\mathbb{N}$ the equation $f(x)=ax$ has a solution.

c) Find all ${a\in\mathbb{N}}$ such that the equation $f(x)=ax$ has a unique solution.
37 replies
Tales
Mar 23, 2005
ezpotd
3 hours ago
J
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AIME qual outside US?
daijobu   10
N Today at 5:23 AM by Yiyj
Can students outside the US take the AIME if they earn a qualifying score?
10 replies
daijobu
Yesterday at 7:10 PM
Yiyj
Today at 5:23 AM
J
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[$10K+ IN PRIZES] Poolesville Math Tournament (PVMT) 2025
qwerty123456asdfgzxcvb   20
N Today at 2:13 AM by panda2018
Hi everyone!

After the resounding success of the first three years of PVMT, the Poolesville High School Math Team is excited to announce the fourth annual Poolesville High School Math Tournament (PVMT)! The PVMT team includes a MOPper and multiple USA(J)MO and AIME qualifiers!

PVMT is open to all 6th-9th graders in the country (including rising 10th graders). Students will compete in teams of up to 4 people, and each participant will take three subject tests as well as the team round. The contest is completely free, and will be held virtually on June 7, 2025, from 10:00 AM to 4:00 PM (EST).

Additionally, thanks to our sponsors, we will be awarding approximately $10K+ worth of prizes (including gift cards, Citadel merch, AoPS coupons, Wolfram licenses) to top teams and individuals. More details regarding the actual prizes will be released as we get closer to the competition date.

Further, newly for this year we might run some interesting mini-events, which we will announce closer to the competition date, such as potentially a puzzle hunt and integration bee!

If you would like to register for the competition, the registration form can be found at https://pvmt.org/register.html or https://tinyurl.com/PVMT25.

Additionally, more information about PVMT can be found at https://pvmt.org

If you have any questions not answered in the below FAQ, feel free to ask in this thread or email us at falconsdomath@gmail.com!

We look forward to your participation!

FAQ
20 replies
qwerty123456asdfgzxcvb
Apr 5, 2025
panda2018
Today at 2:13 AM
J
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Expression is a Cube
nosaj   38
N Today at 1:42 AM by NicoN9
Source: 2015 AIME I Problem 3
There is a prime number $p$ such that $16p+1$ is the cube of a positive integer. Find $p$.
38 replies
nosaj
Mar 20, 2015
NicoN9
Today at 1:42 AM
J
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J
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Math Camps
jack_ma   12
N Apr 20, 2025 by NoSignOfTheta
What are some math camps (residential and online) for high schoolers?
12 replies
jack_ma
Apr 20, 2025
NoSignOfTheta
Apr 20, 2025
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Math Camps
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Reveal topic tags
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jack_ma
8 posts
jack_ma
#1 h  Apr 20, 2025, 2:48 AM
Y by
What are some math camps (residential and online) for high schoolers?
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jack_ma
8 posts
jack_ma
#2 h  Apr 20, 2025, 2:51 AM
Y by
Not limited to summer.
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mdk2013
645 posts
mdk2013
#3 h  Apr 20, 2025, 3:02 AM • 1 Y
Y by ChristianYoo
mop feeling rejected rn
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idk12345678
398 posts
idk12345678
#4 h  Apr 20, 2025, 4:38 AM
Y by
AwesomeMath Summer Program is a camp
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jack_ma
8 posts
jack_ma
#5 h  Apr 20, 2025, 4:04 PM
Y by
bump....
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Pengu14
638 posts
Pengu14
#6 h  Apr 20, 2025, 4:06 PM • 1 Y
Y by jack_ma
MathCamp
HCSSIM
ROSS
PROMYS
SUMAC
AMSP
MathILY
MOP
Z K Y
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jack_ma
8 posts
jack_ma
#8 h  Apr 20, 2025, 4:20 PM
Y by
Pengu14 wrote:
MathCamp
HCSSIM
ROSS
PROMYS
SUMAC
AMSP
MathILY
MOP

whats the difference between MathILY and MathILY-Er?
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jack_ma
8 posts
jack_ma
#9 h  Apr 20, 2025, 4:24 PM • 1 Y
Y by yuanyuanC
is MathIGy real?
This post has been edited 1 time. Last edited by jack_ma, Apr 20, 2025, 4:25 PM
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Turtle09
1817 posts
Turtle09
#10 h  Apr 20, 2025, 4:26 PM • 1 Y
Y by jack_ma
jack_ma wrote:
Pengu14 wrote:
MathCamp
HCSSIM
ROSS
PROMYS
SUMAC
AMSP
MathILY
MOP

whats the difference between MathILY and MathILY-Er?

read the website lmao
it states it's for students who are earlier in their math journeys
jack_ma wrote:
is MathIGy real?

no
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palindrome868
1175 posts
palindrome868
#11 h  Apr 20, 2025, 5:03 PM
Y by
Pengu14 wrote:
MathCamp
HCSSIM
ROSS
PROMYS
SUMAC
AMSP
MathILY
MOP

Pls rank in order of motivation (as in how motivated are the people there).
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idk12345678
398 posts
idk12345678
#12 h  Apr 20, 2025, 5:13 PM
Y by
MOP is probably the most motivated lmao
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profhong
8 posts
profhong
#13 h  Apr 20, 2025, 5:22 PM
Y by
IMC Camp at Charlotte
video highlights: https://youtu.be/GXI0sjkZ_XU?si=B_ZWEfYnxOt4saXv
peace09's journal: https://drive.google.com/file/d/1cenocdEY5Nw56zqNIL4TMCnjTC3yfHMC/view?usp=sharing
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NoSignOfTheta
1749 posts
NoSignOfTheta
#14 h  Apr 20, 2025, 5:25 PM
Y by
idk12345678 wrote:
MOP is probably the most motivated lmao

Nah, AwesomeMath'd win
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