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k a June Highlights and 2025 AoPS Online Class Information

jlacosta 0

Monday at 3:57 PM

Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this 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 a transformative 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][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/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

Monday at 3:57 PM

0 replies

Hide tag workaround

char0221 14

N Today at 5:10 AM by Yrock

Summary of the problem: When quoting a tip tag, hovering over it causes a glitch where the tip tag's inner contents are "stuck" below the quotes.
Page URL: Any community message boards.
Steps to reproduce:
1. Create a message.
2. Insert a quote.
3. Inside the quote, put a tip tag.
4. Submit/preview, then hover over the tip tag.
Expected behavior: Tip tag does not stay when mouse is removed.
Frequency: 100%
Operating system(s): macOS Sequoia
Browser(s), including version: Safari 18.4
Additional information:
IMAGE
Also, make sure that the quote+tip is last.
[quote=char0221]
Try to close me!
[/quote]

14 replies

char0221

May 26, 2025

Yrock

Today at 5:10 AM

Bug on Alcumus

FunnyKoala17 5

N Today at 4:32 AM by FunnyKoala17

Page URL: artofproblemsolving.com/alcumus/problem

Problem: So, I was doing Using Geometry in Probability, and I had a 97 rating. I switched to Arithmetic-Reciprocals. Before, I had a 100 rating in Reciprocals, but then, on another, laptop, I changed back to Arithmetic-Reciprocals, did a question , went back to this laptop, and now, my RECIPROCALS CHANGED FROM 100 TO 97!!

Is this a bug? I'm really sad, cause, it took me a long time to get to 100.

Steps to reproduce: Go on a topic on Laptop 1. Then, do 1 question in Arithmetic-Reciprocals, switch to laptop 2, and switch topics to Using Geometry in Probability. Do one question, switch back to laptop 1, and your Reciprocals rating will change into your Using Geometry in Probability rating.

Frequency: Not often

Expected behavior: It should save your rating, not change it.

Operating system(s): Laptop 1: MacOS Big Sur, version 11.6 Laptop 2: School Chromebook

Browser(s), including version: Idk, Chrome?

Additional information: Laptop 2 was a school chromebook. Nothing else, but the fact that I am VERY SAD. :noo: :noo: :noo:

HOWEVER, PLEASE DON'T TRY TO REPRODUCE UNLESS YOU ARE MOD OR ADMIN. YOU WILL BE VERY SAD, ESPECIALLY THOSE ALCUMUS GRINDERS.

5 replies

FunnyKoala17

Yesterday at 10:22 PM

FunnyKoala17

Today at 4:32 AM

what??????????????????????

Iced_Coffee 20

N Today at 1:52 AM by C4LEricWa

my "my topics" symbol (the little person looking button) and my "bookmarked topics" symbol keep randomly changing to different symbols!!!!!!!! What is happening? the 'my topics' one changed so it looked like it had a gear and a music note and I don't even know what the other one was. this has been happening for two or three days now is it happening to anyone else? please help! :what?:

20 replies

Iced_Coffee

Apr 11, 2025

C4LEricWa

Today at 1:52 AM

PAGE NOT SCROLLING DOWN ALL THE WAY; GETS STUCK 1.5 POSTS BEFORE THREAD END

CurlyFalcon55 11

N Today at 1:01 AM by Demetri

Summary of the problem:
Whenever I push the big, top right "Reply" button– NOT THE SMALL LITTLE "QUICK REPLY" BAR ON THE BOTTOM, and reply, I can't scroll down all the way to the bottom of the thread that I just posted in. Sometimes, very rarely though, I doesn't scroll down all the way when I push the "Quick Reply" bar.

-----Page URL:
Anywhere in the "Introduction to Number Theory" forum in AoPS

-----Steps to reproduce:

1. Go to the link above.

2. Click any thread or create a new one.

3. Click the "Reply" button, not the quick reply bar.

4. Type a reply.

5. Push the "Submit" button.

6. Try to scroll down. if you’re lucky, the problem will reproduce.

-----Expected behavior:
To scroll all the way down.

-----Frequency:
Almost every time I push the big "Reply" button, sometimes (but rarely) when I push the "Quick Reply" bar.

-----Operating system(s):
macOS Sequoia 15.4.1

-----Browser(s), including version:
Chrome, (I don't know what version)

-----Additional information:
-It rarely does it in the "Quick Reply" bar.
-It almost always does it in the big "Reply" button on the top right.

-----Can anyone reproduce?

11 replies

CurlyFalcon55

Jun 1, 2025

Demetri

Today at 1:01 AM

IMC 2009 Day 1 P2

joybangla 3

N Yesterday at 11:23 AM by lminsl

Let $A,B,C$ be real square matrices of the same order, and suppose $A$ is invertible. Prove that
$(A-B)C=BA^{-1}\implies C(A-B)=A^{-1}B$

3 replies

joybangla

Jul 15, 2014

lminsl

Yesterday at 11:23 AM

Expand into a Fourier series

Tip_pay 2

N Yesterday at 10:38 AM by Mathzeus1024

Expand the function in a Fourier series on the interval $(-\pi, \pi)$
$f(x)=\begin{cases} 1, & -1<x\leq 0\\ x, & 0<x<1 \end{cases}$

2 replies

Tip_pay

Dec 12, 2023

Mathzeus1024

Yesterday at 10:38 AM

D1041 : A generalisation of Tchebychef's Inequality

Dattier 1

N Yesterday at 7:37 AM by Dattier

Source: les dattes à Dattier

Let $f,g \in C^1([0,1])$ .

Is it true that : $\min(|f'|)\times \min(|g'|) \leq 12\times \left|\int_0^1f(t)\times g(t) \text{d}t -\int_0^1f(t) \text{d}t\times \int_0^1g(t)\text{d}t\right| \leq \max(|f'|)\times \max(|g'|)$ ?

1 reply

Dattier

Monday at 9:29 PM

Dattier

Yesterday at 7:37 AM

Putnam 2013 A5

Kent Merryfield 10

N Monday at 10:00 PM by blackbluecar

For $m\ge 3,$ a list of $\binom m3$ real numbers $a_{ijk}$ $(1\le i<j<k\le m)$ is said to be area definite for $\mathbb{R}^n$ if the inequality $\sum_{1\le i<j<k\le m}a_{ijk}\cdot\text{Area}(\triangle A_iA_jA_k)\ge0$ holds for every choice of $m$ points $A_1,\dots,A_m$ in $\mathbb{R}^n.$ For example, the list of four numbers $a_{123}=a_{124}=a_{134}=1, a_{234}=-1$ is area definite for $\mathbb{R}^2.$ Prove that if a list of $\binom m3$ numbers is area definite for $\mathbb{R}^2,$ then it is area definite for $\mathbb{R}^3.$

10 replies

Kent Merryfield

Dec 9, 2013

blackbluecar

Monday at 10:00 PM

Reducing the exponents for good

RobertRogo 3

N Monday at 9:22 PM by RobertRogo

Source: The national Algebra contest (Romania), 2025, Problem 3/Abstract Algebra (a bit generalized)

Let $A$ be a ring with unity such that for every $x \in A$ there exist $t_x, n_x \in \mathbb{N}^*$ such that $x^{t_x+n_x}=x^{n_x}$ . Prove that
a) If $t_x \cdot 1 \in U(A), \forall x \in A$ then $x^{t_x+1}=x, \forall x \in A$
b) If there is an $x \in A$ such that $t_x \cdot 1 \notin U(A)$ then the result from a) may no longer hold.

Authors: Laurențiu Panaitopol, Dorel Miheț, Mihai Opincariu, me, Filip Munteanu

3 replies

RobertRogo

May 20, 2025

RobertRogo

Monday at 9:22 PM

If \(\prod_{i=1}^{n} (x + r_i) = \sum_{k=0}^{n} a_k x^k\), show that \[ \sum_{i=

Martin.s 1

N Monday at 7:12 PM by alexheinis

If $\prod_{i=1}^{n} (x + r_i) \equiv \sum_{j=0}^{n} a_j x^{n-i}$ , show that
$\sum_{i=1}^{n} \tan^{-1} r_i = \tan^{-1} \frac{a_1 - a_3 + a_5 - \cdots}{a_0 - a_2 + a_4 - \cdots}$ and
$\sum_{i=1}^{n} \tanh^{-1} r_i = \tanh^{-1} \frac{a_1 + a_3 + a_5 + \cdots}{a_0 + a_2 + a_4 + \cdots}.$

1 reply

Martin.s

Jun 1, 2025

alexheinis

Monday at 7:12 PM

D1040 : A general and strange result

Dattier 1

N Monday at 6:35 PM by Dattier

Source: les dattes à Dattier

Let $f \in C([0,1];[0,1])$ bijective, $f(0)=0$ and $(a_k) \in [0,1]^\mathbb N$ with $\sum \limits_{k=0}^{+\infty} a_k$ converge.

Is it true that $\sum \limits_{k=0}^{+\infty} \sqrt{f(a_k)\times f^{-1}(a_k)}$ converge?

1 reply

Dattier

May 31, 2025

Dattier

Monday at 6:35 PM

functional equation in Z

Matheo_Lucas 2

N Monday at 3:02 PM by mrtheory

Find all functions $f : \mathbb{Z} \to \mathbb{Z}$ such that

$x f(2f(y) - x) + y^2 f(2x - f(y)) = \frac{f(x)^2}{x} + f(y f(y))$
for all $x, y \in \mathbb{Z}$ with $x \neq 0$ .

2 replies

Matheo_Lucas

Jan 11, 2025

mrtheory

Monday at 3:02 PM

Recurrence trouble

SomeonecoolLovesMaths 4

N Monday at 2:48 PM by Hello_Kitty

Let $0 < x_0 < y_0$ be real numbers. Define $x_{n+1} = \frac{x_n + y_n}{2}$ and $y_{n+1} = \sqrt{x_{n+1}y_n}$ .
Prove that $\lim_{n \to \infty} x_n = \lim_{n \to \infty} y_n$ and hence find the limit.

4 replies

SomeonecoolLovesMaths

May 28, 2025

Hello_Kitty

Monday at 2:48 PM

Functions

mclolikoi 3

N Monday at 1:58 PM by Mathzeus1024

Let us consider f as the following function : $f(x)= \frac {x - \sqrt{2}}{ [x \sqrt{2} ] }$

1- Find the definition domain $D_f$

2-Prove that $f$ is continous on $\sqrt{2}$

3-Study the continuity of $f$ on $\frac {3 \sqrt{2} }{2}$

4-Then draw the geometric representation of $f$ on $] \frac {1}{ \sqrt{2} } ; 2 \sqrt{2} [$

3 replies

mclolikoi

Sep 23, 2012

Mathzeus1024

Monday at 1:58 PM

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