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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
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
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
Cute matrix equation
RobertRogo   1
N 9 minutes ago by loup blanc
Source: "Traian Lalescu" student contest 2025, Section A, Problem 2
Find all matrices $A \in \mathcal{M}_n(\mathbb{Z})$ such that $$2025A^{2025}=A^{2024}+A^{2023}+\ldots+A$$
1 reply
RobertRogo
3 hours ago
loup blanc
9 minutes ago
how can I solve this FE
Jackson0423   5
N 22 minutes ago by Jackson0423

Let \( f : \mathbb{R} \to \mathbb{R} \) be a function that satisfies the following equation for all real numbers \( x \):
\[
f(x^2 + x + 3) + 2f(x^2 - 3x + 5) = 6x^2 - 10x + 17.
\]Find the value of \( f(100) \).
5 replies
Jackson0423
an hour ago
Jackson0423
22 minutes ago
Number Theory
VicKmath7   5
N 28 minutes ago by Adywastaken
Source: Archimedes Junior 2014
Let $p$ prime and $m$ a positive integer. Determine all pairs $( p,m)$ satisfying the equation: $ p(p+m)+p=(m+1)^3$
5 replies
VicKmath7
Mar 17, 2020
Adywastaken
28 minutes ago
x+y in B iff x,y in A
fattypiggy123   5
N 32 minutes ago by Math2030
Source: China Mathematical Olympiad 2015 Q3
Let $n \geq 5$ be a positive integer and let $A$ and $B$ be sets of integers satisfying the following conditions:

i) $|A| = n$, $|B| = m$ and $A$ is a subset of $B$
ii) For any distinct $x,y \in B$, $x+y \in B$ iff $x,y \in A$

Determine the minimum value of $m$.
5 replies
fattypiggy123
Dec 20, 2014
Math2030
32 minutes ago
IMO Genre Predictions
ohiorizzler1434   65
N 38 minutes ago by Oksutok
Everybody, with IMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
65 replies
ohiorizzler1434
May 3, 2025
Oksutok
38 minutes ago
k^2/p for k =1 to (p-1)/2
truongphatt2668   1
N an hour ago by Double07
Let $p$ be a prime such that: $p = 4k+1$. Simplify:
$$\sum_{k=1}^{\frac{p-1}{2}}\begin{Bmatrix}\dfrac{k^2}{p}\end{Bmatrix}$$
1 reply
truongphatt2668
3 hours ago
Double07
an hour ago
Interesting inequality
imnotgoodatmathsorry   1
N an hour ago by Bergo1305
Let $x,y,z > \frac{1}{2}$ and $x+y+z=3$.Prove that:
$\sqrt{x^3+y^3+3xy-1}+\sqrt{y^3+z^3+3yz-1}+\sqrt{z^3+x^3+3zx-1}+\frac{1}{4}(x+5)(y+5)(z+5) \le 60$
1 reply
imnotgoodatmathsorry
2 hours ago
Bergo1305
an hour ago
every lucky set of values {a_1,a_2,..,a_n} satisfies a_1+a_2+...+a_n >n2^{n-1}
parmenides51   6
N an hour ago by jonh_malkovich
Source: 2020 International Olympiad of Metropolises P3
Let $n>1$ be a given integer. The Mint issues coins of $n$ different values $a_1, a_2, ..., a_n$, where each $a_i$ is a positive integer (the number of coins of each value is unlimited). A set of values $\{a_1, a_2,..., a_n\}$ is called lucky, if the sum $a_1+ a_2+...+ a_n$ can be collected in a unique way (namely, by taking one coin of each value).
(a) Prove that there exists a lucky set of values $\{a_1, a_2, ..., a_n\}$ with $$a_1+ a_2+...+ a_n < n \cdot 2^n.$$(b) Prove that every lucky set of values $\{a_1, a_2,..., a_n\}$ satisfies $$a_1+ a_2+...+ a_n >n \cdot 2^{n-1}.$$
Proposed by Ilya Bogdanov
6 replies
parmenides51
Dec 19, 2020
jonh_malkovich
an hour ago
A strange NT problem
flower417477   0
an hour ago
Source: unknown
$p$ is a given prime number.$A=\{a_1,a_2,\cdots,a_{p-1}\}$ is a set which $\prod\limits_{i=1}^{p-1}a_i\equiv\frac{p-1}{2}\pmod p$.
Prove that there're at least $\frac{p-1}{2}$ non-empty subsets $B$ of $A$ such that $\sum\limits_{b\in B}b\equiv 1\pmod p$
0 replies
flower417477
an hour ago
0 replies
Group Theory
Stephen123980   1
N an hour ago by alexheinis
Show that if $G_1,G_2$ are two finite groups with $\gcd(|G_1|,|G_2|)=1,$ then show that $Aut(G_1\times G_2)\cong Aut(G_1)\times Aut(G_2).$
1 reply
Stephen123980
4 hours ago
alexheinis
an hour ago
UC Berkeley Integration Bee 2025 Bracket Rounds
Silver08   9
N an hour ago by Silver08
Regular Round

Quarterfinals

Semifinals

3rd Place Match

Finals
9 replies
+1 w
Silver08
Today at 2:26 AM
Silver08
an hour ago
combi/nt
blug   0
an hour ago
Prove that every positive integer $n$ can be written in the form
$$n=2^{a_1}3^{b_1}+2^{a_2}3^{b_2}+..., $$where $a_i, b_j$ are non negative integers, such that
$$2^x3^y\nmid 2^z3^t$$for every $x, y, z, t$.
0 replies
blug
an hour ago
0 replies
Interesting inequalities
sqing   2
N an hour ago by sqing
Source: Own
Let $ a,b,c\geq 0 , a(b+c)=k.$ Prove that
$$\frac{1}{a+1}+\frac{2}{b+1}+\frac{1}{c+1}\geq  \frac{4\sqrt{k}-6}{ k-2}$$Where $5\leq  k\in N^+.$
Let $ a,b,c\geq 0 , a(b+c)=9.$ Prove that
$$\frac{1}{a+1}+\frac{2}{b+1}+\frac{1}{c+1}\geq \frac{6}{7}$$
2 replies
sqing
3 hours ago
sqing
an hour ago
Putnam 2012 A1
Kent Merryfield   14
N 2 hours ago by anudeep
Let $d_1,d_2,\dots,d_{12}$ be real numbers in the open interval $(1,12).$ Show that there exist distinct indices $i,j,k$ such that $d_i,d_j,d_k$ are the side lengths of an acute triangle.
14 replies
Kent Merryfield
Dec 3, 2012
anudeep
2 hours ago
Integration Bee Kaizo
Calcul8er   57
N Today at 2:00 AM by Silver08
Hey integration fans. I decided to collate some of my favourite and most evil integrals I've written into one big integration bee problem set. I've been entering integration bees since 2017 and I've been really getting hands on with the writing side of things over the last couple of years. I hope you'll enjoy!
57 replies
Calcul8er
Mar 2, 2025
Silver08
Today at 2:00 AM
Integration Bee Kaizo
G H J
G H BBookmark kLocked kLocked NReply
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awzhang10
72 posts
#45
Y by
thanks homo_morph AKA Calcul8er very much for the very important hints
SF 3
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awzhang10
72 posts
#46
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SF 5

SF 7
This post has been edited 1 time. Last edited by awzhang10, Mar 16, 2025, 11:10 PM
Reason: wrong problem number
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Calcul8er
20 posts
#47
Y by
awzhang10 wrote:
SF 5

SF 7

Comment on SF 7
This post has been edited 1 time. Last edited by Calcul8er, Mar 17, 2025, 1:35 AM
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awzhang10
72 posts
#48
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SF 6
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Figaro
774 posts
#49
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F.8.
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Calcul8er
20 posts
#50 • 2 Y
Y by aidan0626, franklin2013
Hey all! I thought I'd share the answer sheet (no worked solutions though) so you can verify solutions or potentially gain some insight on how to solve any problems you've been stuck on. I hope you'll enjoy!
Attachments:
Integration_Bee_Kaizo_Answers.pdf (175kb)
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Shikhar_
2 posts
#51
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QF 10
This post has been edited 1 time. Last edited by Shikhar_, Mar 25, 2025, 7:11 PM
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Shikhar_
2 posts
#52
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QF 14
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BaidenMan
1 post
#53
Y by
QR.14.
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franklin2013
283 posts
#54 • 1 Y
Y by aidan0626
This deserves a \bump
As a reminder, these are the integrals that have been solved.
Qualifying Round (FULLY DONE)
Quarterfinals
Semifinals
Finals
This post has been edited 1 time. Last edited by franklin2013, Yesterday at 1:59 PM
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Silver08
460 posts
#56
Y by
Semifinals 14 is botherin me....
Here's my idea:
$$I(n) = \int_0^1 \frac{u^n}{\sqrt{1-u^2}}du = \frac{\sqrt{\pi}\Gamma((n+1)/2)}{2\Gamma(n/2)}$$We want to find $$I^{(3)}(0) = \int_0^{\pi/2}\ln^3(\sin(x))dx.$$But I know nothing about special functions...
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franklin2013
283 posts
#57
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Silver08 wrote:
But I know nothing about special functions...

I knew nothing about calculus and integration until I saw this thread then I attempted to speedrun calc 1 and 2 and succeeded (i guess)
This post has been edited 1 time. Last edited by franklin2013, Wednesday at 8:28 PM
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Figaro
774 posts
#59
Y by
@Silver08: regarding SF14, this might interest you:

https://www.youtube.com/watch?v=f9pR30LRnzs&list=PL22w63XsKjqzJpcuD6InKWZXep2L0z1H8&index=6
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franklin2013
283 posts
#61
Y by
I got inspired by Qualifying Round 4's solution, and quickly found the answer to this.

$$I=\int^1_0\left(\left\lfloor\frac{1}{\sqrt[69]{x}}\right\rfloor-420\left\lfloor\frac{1}{420\sqrt[69]{x}}\right\rfloor\right)dx$$Finals 5
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Silver08
460 posts
#62
Y by
Figaro wrote:

Ewwwwww, Apery's constant!! >:V
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