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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

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]
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

May 1, 2025

0 replies

Fractional Inequality

sqing 33

Source: Chinese Girls Mathematical Olympiad 2012, Problem 1

Let $a_1, a_2,\ldots, a_n$ be non-negative real numbers. Prove that
$\frac{1}{1+ a_1}+\frac{ a_1}{(1+ a_1)(1+ a_2)}+\frac{ a_1 a_2}{(1+ a_1)(1+ a_2)(1+ a_3)}+$ $\cdots+\frac{ a_1 a_2\cdots a_{n-1}}{(1+ a_1)(1+ a_2)\cdots (1+ a_n)} \le 1.$

33 replies

1 viewing

sqing

Aug 10, 2012

Learning11

a few seconds ago

Geometry angle chasing olympiads

Foxellar 1

Let $\triangle ABC$ be a triangle such that $\angle ABC = 120^\circ$ . Points $X, Y, Z$ lie on segments $BC, CA, AB$ , respectively, such that lines $AX, BY,$ and $CZ$ are the angle bisectors of triangle $ABC$ . Find the measure of angle $\angle XYZ$ .

1 reply

Foxellar

33 minutes ago

Ianis

24 minutes ago

Iran Inequality

mathmatecS 17

Source: Iran 1998

When $x(\ge1),$ $y(\ge1),$ $z(\ge1)$ satisfy $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2,$ prove in equality.
$\sqrt{x+y+z}\ge\sqrt{x-1}+\sqrt{y-1}+\sqrt{z-1}$

17 replies

mathmatecS

Jun 11, 2015

Learning11

26 minutes ago

Problem 4

codyj 87

Source: IMO 2015 #4

Triangle $ABC$ has circumcircle $\Omega$ and circumcenter $O$ . A circle $\Gamma$ with center $A$ intersects the segment $BC$ at points $D$ and $E$ , such that $B$ , $D$ , $E$ , and $C$ are all different and lie on line $BC$ in this order. Let $F$ and $G$ be the points of intersection of $\Gamma$ and $\Omega$ , such that $A$ , $F$ , $B$ , $C$ , and $G$ lie on $\Omega$ in this order. Let $K$ be the second point of intersection of the circumcircle of triangle $BDF$ and the segment $AB$ . Let $L$ be the second point of intersection of the circumcircle of triangle $CGE$ and the segment $CA$ .

Suppose that the lines $FK$ and $GL$ are different and intersect at the point $X$ . Prove that $X$ lies on the line $AO$ .

Proposed by Greece

87 replies

codyj

Jul 11, 2015

ezpotd

43 minutes ago

College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

Prove the statement

Butterfly 13

Given an infinite sequence $\{x_n\} \subseteq [0,1]$ , there exists some constant $C$ , for any $r>0$ , among the sequence $x_n$ and $x_m$ could be chosen to satisfy $|n-m|\ge r$ and $|x_n-x_m|<\frac{C}{|n-m|}$ .

13 replies

Butterfly

May 7, 2025

oty

an hour ago

D1038 : A generalization of Jensen

Dattier 3

Source: les dattes à Dattier

Let $f \in C^1([0,1]), g \in C^2(f([0;1]))$ .

Is it true that

$\min(|g''|)\times \min(|f'|^2) \leq 24 \times\left|\int_0^1g(f(x)) \text{d}x- g(\int_0^1 f(x) \text{d}x) \right| \leq \max(|g''|)\times \max(|f'|^2)$ ?

3 replies

Dattier

Today at 12:15 PM

greenturtle3141

an hour ago

3rd AKhIMO for University Students, P2

UzbekMathematician 1

Source: AKhIMO 2025, P2

Find all possible values of $gcd(a^{2m}+1, a^n+1)$ , where $a, m, n$ are positive integers and $n$ is odd.

1 reply

UzbekMathematician

Today at 1:48 PM

grupyorum

an hour ago

Problem 2, Grade 12th RMO Shortlist - Year 2002

sticknycu 5

Let $A \in M_2(C), A \neq O_2, A \neq I_2, n \in \mathbb{N}^*$ and $S_n = \{ X \in M_2(C) | X^n = A \}$ .
Show:
a) $S_n$ with multiplication of matrixes operation is making an isomorphic-group structure with $U_n$ .
b) $A^2 = A$ .

Marian Andronache

5 replies

sticknycu

Jan 3, 2020

P_Fazioli

Today at 4:07 PM

Featured Content

Problem of the Day 2018 Vietnam Team Selection Test

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In a $m\times n$ square grid, with top-left corner is $A$ , there is route along the edges of the grid starting from $A$ and visits all lattice points (called "nodes") exactly once and ending also at $A$ .

a. Prove that this route exists if and only if at least one of $m,\ n$ is odd.
b. If such a route exists, then what is the least possible of turning points?

*A turning point is a node that is different from $A$ and if two edges on the route intersect at the node are perpendicular.

gausskarl

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Contest of the Week 2023 Canada National Olympiad

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2023 Canada National Olympiad

William is thinking of an integer between 1 and 50, inclusive. Victor can choose a positive integer $m$ and ask William: "does $m$ divide your number?", to which William must answer truthfully. Victor continues asking these questions until he determines William's number. What is the minimum number of questions that Victor needs to guarantee this?

eduD_looC

view topic

There are 20 students in a high school class, and each student has exactly three close friends in the class. Five of the students have bought tickets to an upcoming concert. If any student sees that at least two of their close friends have bought tickets, then they will buy a ticket too.

Is it possible that the entire class buys tickets to the concert?

(Assume that friendship is mutual; if student $A$ is close friends with student $B$ , then $B$ is close friends with $A$ .)

eduD_looC

view topic

An acute triangle is a triangle that has all angles less than $90^{\circ}$ ( $90^{\circ}$ is a Right Angle). Let $ABC$ be an acute triangle with altitudes $AD$ , $BE$ , and $CF$ meeting at $H$ . The circle passing through points $D$ , $E$ , and $F$ meets $AD$ , $BE$ , and $CF$ again at $X$ , $Y$ , and $Z$ respectively. Prove the following inequality: $\frac{AH}{DX}+\frac{BH}{EY}+\frac{CH}{FZ} \geq 3.$

eduD_looC

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Let $f(x)$ be a non-constant polynomial with integer coefficients such that $f(1) \neq 1$ . For a positive integer $n$ , define $\text{divs}(n)$ to be the set of positive divisors of $n$ .

A positive integer $m$ is $f$ -cool if there exists a positive integer $n$ for which $f[\text{divs}(m)]=\text{divs}(n).$ Prove that for any such $f$ , there are finitely many $f$ -cool integers.

(The notation $f[S]$ for some set $S$ denotes the set $\{f(s):s \in S\}$ .)

eduD_looC

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

May 1, 2025

0 replies

k Weird FTW game??

TheCoinNinja 3

What is going on with this game??
As far as I can tell, this 10-problem, 45-second game has been sitting here with 1 of 1 players participating, and yet not started, for a long time. Also, I_am_a_penguin has a normal avatar, not the gray one.

Summary of the problem: This should not be possible. The game should have started when the user created it since it's just a one person game.
Page URL:aops.com/ftw/ftw
Expected behavior: The game should have either started or disappeared.
Frequency: 100%
Operating system(s): Windows 11
Browser(s), including version: Chrome and Firefox

3 replies

TheCoinNinja

Today at 1:20 AM

jlacosta

3 hours ago

k AoPS Report Bar

Svnshiin3-QTPI 5

Hello there!
This is my first AoPS class, and I was wondering why my report bar is orange.
I have completed all of the Challenge homework problems, as well as the writing problems.
Is this because the writing problems have not been graded yet?
If not, are there any other assignments I need to complete?
Thanks.

(edit: resolved)

5 replies

Svnshiin3-QTPI

Today at 4:01 AM

jlacosta

3 hours ago

Stamina XP decreasing?

Craftybutterfly 29

Summary of the problem: Last night when I checked, alcumus said I had 4250 stamina XP which is more than other people. However, when I just checked, it said I only earned 3905 XP. What is wrong?
Page URL: Hall of Fame
Steps to reproduce:
1. Go to hall of fame
2. Scroll to stamina XP earned
Expected behavior: It should still say I earned 4250 XP
Frequency: 100%
Operating system(s): HP Elitebook
Browser(s), including version: Chrome
IMAGE

29 replies

Craftybutterfly

May 22, 2025

Craftybutterfly

Today at 3:11 AM

Hide tag workaround

char0221 6

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]

6 replies

char0221

May 26, 2025

jlacosta

Yesterday at 10:56 PM

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2025 Bulgarian Winter Tournament
Bulgarian Winter Tournament 2025

2025 Bundeswettbewerb Mathematik
Bundeswettbewerb Mathematik 2025

2025 Canada Junior National Olympiad
Canada Junior National Olympiad 2025

2025 Canada National Olympiad
Canada National Olympiad 2025

2025 Caucasus Mathematical Olympiad
X Caucasus Mathematical Olympiad

2025 China National Olympiad
2025 China National Olympiad

2025 China Team Selection Test
China Team Selection Test 2025

2025 EGMO
European Girls MO 2025

2025 Euler Olympiad

2025 Francophone Mathematical Olympiad
Math olympiad for the French Speaking, 2025

2025 Greece National Olympiad
2025 Greece National Olympiad

2025 India National Olympiad
India National Olympiad 2025

2025 India STEMS

2025 International Zhautykov Olympiad
International Zhautykov Olympiad 2025

2025 Iran MO (2nd Round)
National Math Olympiad (Second Round) 2025

2025 Israel National Olympiad (Gillis)
An Olympiad for grades 7-12.

2025 Israel TST

2025 Japan MO Finals
Japan MO Finals 2025

2025 Korea - Final Round
FKMO 2025

2025 Korea Winter Program Practice Test
Korea Winter Program Practice Test 2025

2025 Kyiv City MO Round 1
Problems from first round of Kyiv Mathematical Olympiad 2025

2025 Kyiv City MO Round 2
Problems from second round of Kyiv Mathematical Olympiad 2025

2025 Macedonian Mathematical Olympiad
The problems from the 32nd Macedonian Mathematical Olympiad

2025 Macedonian TST
The problems from the 2025 Macedonian TST

2025 Malaysian APMO Camp Selection Test
Malaysian APMO Camp Selection Test for APMO 2025

2025 Nordic
Nordic 2025

2025 Philippine MO

2025 Poland - First Round

2025 Poland - Second Round
Second Round - Poland 2025

2025 Polish MO Finals
Polish MO Finals 2025

2025 Portugal MO
Portugal MO 2025

2025 Romanian Master of Mathematics
15th RMM 2025

2025 Sharygin Geometry Olympiad
Sharygin Geometry Olympiad 2025

2025 Spain Mathematical Olympiad
Spain Mathematical Olympiad 2025

2025 Taiwan TST Round 1

2025 Taiwan TST Round 2
Taiwan TST Round 2 2025

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