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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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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)!

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[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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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]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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Dear Sqing: So Many Inequalities...
hashtagmath   37
N 5 minutes ago by hashtagmath
I have noticed thousands upon thousands of inequalities that you have posted to HSO and was wondering where you get the inspiration, imagination, and even the validation that such inequalities are true? Also, what do you find particularly appealing and important about specifically inequalities rather than other branches of mathematics? Thank you :)
37 replies
hashtagmath
Oct 30, 2024
hashtagmath
5 minutes ago
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integer functional equation
ABCDE   148
N 15 minutes ago by Jakjjdm
Source: 2015 IMO Shortlist A2
Determine all functions $f:\mathbb{Z}\rightarrow\mathbb{Z}$ with the property that \[f(x-f(y))=f(f(x))-f(y)-1\]holds for all $x,y\in\mathbb{Z}$.
148 replies
ABCDE
Jul 7, 2016
Jakjjdm
15 minutes ago
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IMO Shortlist 2013, Number Theory #1
lyukhson   152
N 36 minutes ago by Jakjjdm
Source: IMO Shortlist 2013, Number Theory #1
Let $\mathbb{Z} _{>0}$ be the set of positive integers. Find all functions $f: \mathbb{Z} _{>0}\rightarrow \mathbb{Z} _{>0}$ such that
\[ m^2 + f(n) \mid mf(m) +n \]
for all positive integers $m$ and $n$.
152 replies
1 viewing
lyukhson
Jul 10, 2014
Jakjjdm
36 minutes ago
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9x9 Board
mathlover314   8
N 37 minutes ago by sweetbird108
There is a $9x9$ board with a number written in each cell. Every two neighbour rows sum up to at least $20$, and every two neighbour columns sum up to at most $16$. Find the sum of all numbers on the board.
8 replies
mathlover314
May 6, 2023
sweetbird108
37 minutes ago
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Equation over a finite field
loup blanc   1
N 3 hours ago by alexheinis
Find the set of $x\in\mathbb{F}_{5^5}$ such that the equation in the unknown $y\in \mathbb{F}_{5^5}$:
$x^3y+y^3+x=0$ admits $3$ roots: $a,a,b$ s.t. $a\not=b$.
1 reply
loup blanc
6 hours ago
alexheinis
3 hours ago
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Integration Bee Kaizo
Calcul8er   51
N 4 hours ago by BaidenMan
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!
51 replies
Calcul8er
Mar 2, 2025
BaidenMan
4 hours ago
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interesting integral
Martin.s   1
N Yesterday at 2:46 PM by ysharifi
$$\int_0^\infty \frac{\sinh(t)}{t \cosh^3(t)} dt$$
1 reply
Martin.s
Monday at 3:12 PM
ysharifi
Yesterday at 2:46 PM
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Two times derivable real function
Valentin Vornicu   10
N Yesterday at 2:04 PM by Rohit-2006
Source: RMO 2008, 11th Grade, Problem 3
Let $ f: \mathbb R \to \mathbb R$ be a function, two times derivable on $ \mathbb R$ for which there exist $ c\in\mathbb R$ such that
\[ \frac { f(b)-f(a) }{b-a} \neq f'(c) ,\] for all $ a\neq b \in \mathbb R$.

Prove that $ f''(c)=0$.
10 replies
Valentin Vornicu
Apr 30, 2008
Rohit-2006
Yesterday at 2:04 PM
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Find the volume of the solid
r02246013   3
N Yesterday at 12:36 PM by Mathzeus1024
Find the volume of the solid bounded by the graphs of $z=\sqrt{x^2+y^2}$, $z=0$ and $x^2+y^2=25$.
3 replies
r02246013
Dec 16, 2017
Mathzeus1024
Yesterday at 12:36 PM
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Find the greatest possible value of the expression
BEHZOD_UZ   0
Yesterday at 11:56 AM
Source: Yandex Uzbekistan Coding and Math Contest 2025
Let $a, b, c, d$ be complex numbers with $|a| \le 1, |b| \le 1, |c| \le 1, |d| \le 1$. Find the greatest possible value of the expression $$|ac+ad+bc-bd|.$$
0 replies
BEHZOD_UZ
Yesterday at 11:56 AM
0 replies
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high school math
aothatday   8
N Yesterday at 1:09 AM by EthanNg6
Let $x_n$ be a positive root of the equation $x^n=x^2+x+1$. Prove that the following sequence converges: $n^2(x_n-x_{ n+1})$
8 replies
aothatday
Apr 10, 2025
EthanNg6
Yesterday at 1:09 AM
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Why is this series not the Fourier series of some Riemann integrable function
tohill   1
N Monday at 11:53 PM by alexheinis
$\sum_{n=1}^{\infty}{\frac{\sin nx}{\sqrt{n}}}$ (0<x<2π)
1 reply
tohill
Monday at 8:08 AM
alexheinis
Monday at 11:53 PM
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Research Opportunity
dinowc   0
Monday at 10:17 PM
Hi everyone, my name is William Chang and I'm a second year phd student at UCLA studying applied math. Over the past year, I've mentored many undergraduates at UCLA to finished papers (currently under review) in reinforcement learning (see here. :juggle:)

I'm looking to expand my group (and the topics I'm studying) so if you're interested, please let me know. I would especially encourage you to reach out to me chang314@g.ucla.edu if you like math. :wow:
0 replies
dinowc
Monday at 10:17 PM
0 replies
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Computational Calculus - SMT 2025
Munmun5   3
N Monday at 9:58 PM by alexheinis
Source: SMT 2025
1. Consider the set of all continuous and infinitely differentiable functions $f$ with domain $[0,2025]$ satisfying $$f(0)=0,f'(0)=0,f'(2025)=1$$and $f''$ is strictly increasing on $[0,2025]$ Compute smallest real M such that all functions in this set ,$f(2025)<M$ .
2. Polynomials $$A(x)=ax^3+abx^2-4x-c$$$$B(x)=bx^3+bcx^2-6x-a$$$$C(x)=cx^3+cax^2-9x-b$$have local extrema at $b,c,a$ respectively. find $abc$ . Here $a,b,c$ are constants .
3. Let $R$ be the region in the complex plane enclosed by curve $$f(x)=e^{ix}+e^{2ix}+\frac{e^{3ix}}{3}$$for $0\leq x\leq 2\pi$. Compute perimeter of $R$ .
3 replies
Munmun5
Monday at 9:35 AM
alexheinis
Monday at 9:58 PM
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Root comparing by Viete
giangtruong13   1
N Apr 14, 2025 by RagvaloD
Given equation $ax^2+bx+c=0$ has 2 roots $m,n$ and equation $cx^2+dx+a=0$ has 2 roots called $p,q$. Prove that $$m^2+n^2+p^2+q^2 \geq 4$$
1 reply
giangtruong13
Apr 14, 2025
RagvaloD
Apr 14, 2025
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Root comparing by Viete
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Reveal topic tags
inequalities
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giangtruong13
128 posts
giangtruong13
#1 h  Apr 14, 2025, 3:00 PM
Y by
Given equation $ax^2+bx+c=0$ has 2 roots $m,n$ and equation $cx^2+dx+a=0$ has 2 roots called $p,q$. Prove that $$m^2+n^2+p^2+q^2 \geq 4$$
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RagvaloD
4909 posts
RagvaloD
#2 h  Apr 14, 2025, 5:30 PM
Y by
$m^2+n^2+p^2+q^2 \geq 2|mn|+2|pq| = 2( |\frac{c}{a}|+|\frac{a}{c}|) \geq 4$
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