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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)!

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[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
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Old problem
kwin   1
N 14 minutes ago by Nguyenhuyen_AG
Let $ a, b, c > 0$ . Prove that:
$$(a^2+b^2)(b^2+c^2)(c^2+a^2)(ab+bc+ca)^2 \ge 8(abc)^2(a^2+b^2+c^2)^2$$
1 reply
kwin
5 hours ago
Nguyenhuyen_AG
14 minutes ago
J
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LCM genius problem from our favorite author
MS_Kekas   1
N 31 minutes ago by Tintarn
Source: Kyiv City MO 2022 Round 2, Problem 8.1
Find all triples $(a, b, c)$ of positive integers for which $a + [a, b] = b + [b, c] = c + [c, a]$.

Here $[a, b]$ denotes the least common multiple of integers $a, b$.

(Proposed by Mykhailo Shtandenko)
1 reply
MS_Kekas
Jan 30, 2022
Tintarn
31 minutes ago
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IMO Solution mistake
CHESSR1DER   0
44 minutes ago
Source: Mistake in IMO 1982/1 4th solution
I found a mistake in 4th solution at IMO 1982/1. It gives answer $660$ and $661$. But right answer is only $660$. Should it be reported somewhere in Aops?
0 replies
CHESSR1DER
44 minutes ago
0 replies
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All the numbers to be zero after finitely many operations
orl   9
N 2 hours ago by User210790
Source: IMO Shortlist 1989, Problem 19, ILL 64
A natural number is written in each square of an $ m \times n$ chess board. The allowed move is to add an integer $ k$ to each of two adjacent numbers in such a way that non-negative numbers are obtained. (Two squares are adjacent if they have a common side.) Find a necessary and sufficient condition for it to be possible for all the numbers to be zero after finitely many operations.
9 replies
orl
Sep 18, 2008
User210790
2 hours ago
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Inequalities
sqing   8
N 6 hours ago by sqing
Let $a,b,c >2 $ and $ ab+bc+ca \leq 75.$ Show that
$$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 1$$Let $a,b,c >2 $ and $ \frac{1}{a}+\frac{1}{b}+\frac{1}{c}\geq \frac{6}{7}.$ Show that
$$\frac{1}{a-2}+\frac{1}{b-2}+\frac{1}{c-2}\geq 2$$
8 replies
sqing
May 13, 2025
sqing
6 hours ago
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trigonometric functions
VivaanKam   16
N Today at 1:03 AM by Shan3t
Hi could someone explain the basic trigonometric functions to me like sin, cos, tan etc.
Thank you!
16 replies
VivaanKam
Apr 29, 2025
Shan3t
Today at 1:03 AM
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Minimum number of points
Ecrin_eren   2
N Yesterday at 8:32 PM by Shan3t
There are 18 teams in a football league. Each team plays against every other team twice in a season—once at home and once away. A win gives 3 points, a draw gives 1 point, and a loss gives 0 points. One team became the champion by earning more points than every other team. What is the minimum number of points this team could have?

2 replies
Ecrin_eren
Yesterday at 4:09 PM
Shan3t
Yesterday at 8:32 PM
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Weird locus problem
Sedro   7
N Yesterday at 8:00 PM by ReticulatedPython
Points $A$ and $B$ are in the coordinate plane such that $AB=2$. Let $\mathcal{H}$ denote the locus of all points $P$ in the coordinate plane satisfying $PA\cdot PB=2$, and let $M$ be the midpoint of $AB$. Points $X$ and $Y$ are on $\mathcal{H}$ such that $\angle XMY = 45^\circ$ and $MX\cdot MY=\sqrt{2}$. The value of $MX^4 + MY^4$ can be expressed in the form $\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
7 replies
Sedro
May 11, 2025
ReticulatedPython
Yesterday at 8:00 PM
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IOQM P23 2024
SomeonecoolLovesMaths   3
N Yesterday at 4:53 PM by lakshya2009
Consider the fourteen numbers, $1^4,2^4,...,14^4$. The smallest natural numebr $n$ such that they leave distinct remainders when divided by $n$ is:
3 replies
SomeonecoolLovesMaths
Sep 8, 2024
lakshya2009
Yesterday at 4:53 PM
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Inequalities
sqing   2
N Yesterday at 4:05 PM by MITDragon
Let $ 0\leq x,y,z\leq 2. $ Prove that
$$-48\leq (x-yz)( 3y-zx)(z-xy)\leq 9$$$$-144\leq (3x-yz)(y-zx)(3z-xy)\leq\frac{81}{64}$$$$-144\leq (3x-yz)(2y-zx)(3z-xy)\leq\frac{81}{16}$$
2 replies
sqing
May 9, 2025
MITDragon
Yesterday at 4:05 PM
J
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Pells equation
Entrepreneur   0
Yesterday at 3:56 PM
A Pells Equation is defined as follows $$x^2-1=ky^2.$$Where $x,y$ are positive integers and $k$ is a non-square positive integer. If $(x_n,y_n)$ denotes the n-th set of solution to the equation with $(x_0,y_0)=(1,0).$ Then, prove that $$x_{n+1}x_n-ky_{n+1}y_n=x_1,$$$$x_n\pm y_n\sqrt k=(x_1\pm y_1\sqrt k)^n.$$
0 replies
Entrepreneur
Yesterday at 3:56 PM
0 replies
J
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Incircle concurrency
niwobin   1
N Yesterday at 2:42 PM by niwobin
Triangle ABC with incenter I, incircle is tangent to BC, AC, and AB at D, E and F respectively.
DT is a diameter for the incircle, and AT meets the incircle again at point H.
Let DH and EF intersect at point J. Prove: AJ//BC.
1 reply
niwobin
May 11, 2025
niwobin
Yesterday at 2:42 PM
J
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Inequalities
sqing   3
N Yesterday at 2:29 PM by rachelcassano
Let $ a,b,c>0 $ . Prove that
$$\frac{a+5b}{b+c}+\frac{b+5c}{c+a}+\frac{c+5a}{a+b}\geq 9$$$$ \frac{2a+11b}{b+c}+\frac{2b+11c}{c+a}+\frac{2c+11a}{a+b}\geq \frac{39}{2}$$$$ \frac{25a+147b}{b+c}+\frac{25b+147c}{c+a}+\frac{25c+147a}{a+b} \geq258$$
3 replies
sqing
May 14, 2025
rachelcassano
Yesterday at 2:29 PM
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The centroid of ABC lies on ME [2023 Abel, Problem 1b]
Amir Hossein   3
N Yesterday at 1:45 PM by Captainscrubz
In the triangle $ABC$, points $D$ and $E$ lie on the side $BC$, with $CE = BD$. Also, $M$ is the midpoint of $AD$. Show that the centroid of $ABC$ lies on $ME$.
3 replies
Amir Hossein
Mar 12, 2024
Captainscrubz
Yesterday at 1:45 PM
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Jiho placing tulips
hanulyeongsam   0
Apr 19, 2025
Source: own
Jiho will choose 46 holes in a 9X9 holebox. Jiho will then place tulips on the holes. Prove that for every 2X2, there is one that has more than 2 tulips inside.
0 replies
hanulyeongsam
Apr 19, 2025
0 replies
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Jiho placing tulips
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hanulyeongsam
170 posts
hanulyeongsam
#1 h  Apr 19, 2025, 3:00 PM
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Jiho will choose 46 holes in a 9X9 holebox. Jiho will then place tulips on the holes. Prove that for every 2X2, there is one that has more than 2 tulips inside.
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