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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]
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0 replies

jlacosta

May 1, 2025

0 replies

Set of prime divisors are same!

mojyla222 6

Source: Iran 2024 3rd round number theory exam p2

For all positive integers $n$ Prove that one can find pairwise coprime integers $a,b,c>n$ such that the set of prime divisors of the numbers $a+b+c$ and $ab+bc+ac$ coincides.

Proposed by Mohsen Jamali and Hesam Rajabzadeh

6 replies

mojyla222

Aug 27, 2024

MR.1

10 minutes ago

collinearity wanted, 2 intersecting circles tangent to 3rd circle and it's chord

parmenides51 1

Source: 2008 Italy TST 1.3

Let $ABC$ be an acute triangle, let $AM$ be a median, and let $BK$ and $CL$ be the altitudes. Let $s$ be the line perpendicular to $AM$ passing through $A$ . Let $E$ be the intersection point of $s$ with $CL$ , and let $F$ be the intersection point of $s$ with $BK$ .
(a) Prove that $A$ is the midpoint of $EF$ .
(b) Let $\Gamma$ be the circumscribed circle of the triangle $MEF$ , and let $\Gamma_1$ and $\Gamma_2$ be any two circles that have two points $P$ and $Q$ in common, and are tangent to the segment $EF$ and the arc $EF$ of $\Gamma$ not containing the point $M$ . Prove that points $M, P, Q$ are collinear.

1 reply

parmenides51

Sep 25, 2020

SuperBarsh

23 minutes ago

Interesting inequalities

sqing 2

Source: Own

Let $a,b >0$ and $a^2-ab+b^2\leq 1$ . Prove that
$a^4 +b^4+\frac{a }{b +1}+ \frac{b }{a +1} \leq 3$ $a^3 +b^3+\frac{a^2}{b^2+1}+ \frac{b^2}{a^2+1} \leq 3$ $a^4 +b^4-\frac{a}{b+1}-\frac{b}{a+1} \leq 1$ $a^4+b^4 -\frac{a^2}{b^2+1}- \frac{b^2}{a^2+1}\leq 1$ $a^3+b^3 -\frac{a^3}{b^3+1}- \frac{b^3}{a^3+1}\leq 1$

2 replies

sqing

May 9, 2025

ytChen

37 minutes ago

3 var inequality

SunnyEvan 2

Let $a,b,c \in R$ ,such that $a^2+b^2+c^2=4(ab+bc+ca)$ Prove that : $\frac{53}{2}-9\sqrt{14} \leq \frac{8(a^3b+b^3c+c^3a)}{27(a^2+b^2+c^2)^2} \leq \frac{53}{2}+9\sqrt{14}$

2 replies

SunnyEvan

3 hours ago

sqing

an hour 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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114,288 topics

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

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jlacosta

May 1, 2025

0 replies

fibonacci number theory

FFA21 1

Source: OSSM Comp'25 P3 (HSE IMC qualification)

$F_n$ fibonacci numbers ( $F_1=1, F_2=1$ ) find all n such that:
$\forall i\in Z$ and $0\leq i\leq F_n$
$C^i_{F_n}\equiv (-1)^i\pmod{F_n+1}$

1 reply

FFA21

May 14, 2025

alexheinis

2 hours ago

Proving a group is abelian

dragosgamer12 8

Source: Florin Stanescu, Gazeta Matematica seria B Nr.2/2025

Let $(G,\cdot)$ be a group, $K$ a subgroup of $G$ and $f : G \rightarrow G$ an endomorphism with the following property:
There exists a nonempty set $H\subset G$ such that for any $k \in G \setminus K$ there exist $h \in H$ with $f(h)=k$ and $z \cdot h= h \cdot z$ , for any $z \in H$ .

a)Prove that $(G, \cdot)$ is abelian.
b)If, additionally, $H$ is a subgroup of $G$ , prove that $H=G$

8 replies

dragosgamer12

Thursday at 10:06 PM

dragosgamer12

Today at 10:14 AM

A challenging sum

Polymethical_ 1

I tried to integrate series of log(1-x) / x

1 reply

Polymethical_

Today at 4:09 AM

Polymethical_

Today at 4:16 AM

Tough integral

Martin.s 3

$\int_0^{\pi/2}\ln(\tan(\theta/2)) \;\frac{4\cos\theta\cos(2\theta)}{4\sin^4\theta+1}\,d\theta.$

3 replies

Martin.s

May 12, 2025

GreenKeeper

Yesterday at 9:42 PM

Featured Content

Problem of the Day 2018 Finnish National High School Mathematics Comp

2018 Finnish National High School Mathematics Comp

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Problem of the Day 2018 Finnish National High School Mathematics Comp

2018 Finnish National High School Mathematics Comp

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2018 Finnish National High School Mathematics Comp

The chords $AB$ and $CD$ of a circle intersect at $M$ , which is the midpoint of the chord $PQ$ . The points $X$ and $Y$ are the intersections of the segments $AD$ and $PQ$ , respectively, and $BC$ and $PQ$ , respectively. Show that $M$ is the midpoint of $XY$ .

parmenides51

view topic

Contest of the Week 1992 Canada National Olympiad

1992 Canada National Olympiad

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Contest of the Week 1992 Canada National Olympiad

1992 Canada National Olympiad

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1992 Canada National Olympiad

Prove that the product of the first $n$ natural numbers is divisible by the sum of the first $n$ natural numbers if and only if $n+1$ is not an odd prime.

Silverfalcon

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For $x,y,z \geq 0,$ establish the inequality

$x(x-z)^2 + y(y-z)^2 \geq (x-z)(y-z)(x+y-z)$

and determine when equality holds.

Silverfalcon

view topic

In the diagram, $ABCD$ is a square, with $U$ and $V$ interior points of the sides $AB$ and $CD$ respectively. Determine all the possible ways of selecting $U$ and $V$ so as to maximize the area of the quadrilateral $PUQV$ .

//cdn.artofproblemsolving.com/images/adf30de296d208bb2f36792cf94608619204b78f.jpg

//cdn.artofproblemsolving.com/images/adf30de296d208bb2f36792cf94608619204b78f.jpg

Silverfalcon

view topic

Solve the equation

$x^2 + \frac{x^2}{(x+1)^2} = 3$

Silverfalcon

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k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

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jlacosta

May 1, 2025

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Introducing myself at AoPS, and what's your magic wand?

asuth_asuth 1176

Hi!

I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.

Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops

I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.

1176 replies

+1 w

asuth_asuth

Mar 30, 2025

MathNinja9

5 minutes ago

All Topics Marked

alpha31415 1

Excuse me!
for I am a frashman in aops.I wonder how I could get back to mark all my read.All topics in the forum became as if they had been marked.Would someone please help me deal with it???

1 reply

alpha31415

Yesterday at 12:39 PM

jmr2010

Yesterday at 6:10 PM

k profile pictures

happymoose666 1

I'm pretty sure this question was raised before but why are their two different avatars?

1 reply

happymoose666

Thursday at 11:10 PM

RollingPanda4616

Thursday at 11:24 PM

k Glitch or Bug?

awesometriangles 5

I was asking for some $\LaTeX$ help in one of my classrooms, and one of the Halpers posted. Is this a glitch or a bug(see screenshot)?

It seems as though I can edit their post...

5 replies

awesometriangles

May 14, 2025

Craftybutterfly

May 14, 2025

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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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