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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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d1-d2 divides n for all divisors d1, d2
a_507_bc   6
N 4 minutes ago by Assassino9931
Source: Romania 3rd JBMO TST 2023 P1
Determine all natural numbers $n \geq 2$ with at most four natural divisors, which have the property that for any two distinct proper divisors $d_1$ and $d_2$ of $n$, the positive integer $d_1-d_2$ divides $n$.
6 replies
a_507_bc
May 20, 2023
Assassino9931
4 minutes ago
J
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Good divisors and special numbers.
Nuran2010   4
N 6 minutes ago by Assassino9931
Source: Azerbaijan Al-Khwarizmi IJMO TST 2024
$N$ is a positive integer. Call all positive divisors of $N$ which are different from $1$ and $N$ beautiful divisors.We call $N$ a special number when it has at least $2$ beautiful divisors and difference of any $2$ beautiful divisors divides $N$ as well. Find all special numbers.
4 replies
Nuran2010
Apr 29, 2025
Assassino9931
6 minutes ago
J
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Hard math inequality
noneofyou34   0
7 minutes ago
If a,b,c are positive real numbers, such that a+b+c=1. Prove that:
(b+c)(a+c)/(a+b)+ (b+a)(a+c)/(c+b)+(b+c)(a+b)/(a+c)>= Sqrt.(6(a(a+c)+b(a+b)+c(b+c)) +3
0 replies
noneofyou34
7 minutes ago
0 replies
J
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Interesting inequalities
sqing   4
N 13 minutes ago by pooh123
Source: Own
Let $a,b,c \geq 0 $ and $ab+bc+ca- abc =3.$ Show that
$$a+k(b+c)\geq 2\sqrt{3 k}$$Where $ k\geq 1. $
Let $a,b,c \geq 0 $ and $2(ab+bc+ca)- abc =31.$ Show that
$$a+k(b+c)\geq \sqrt{62k}$$Where $ k\geq 1. $
4 replies
sqing
May 16, 2025
pooh123
13 minutes ago
J
No more topics!
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angle wanted, right angle inside a square
parmenides51   1
N Jan 23, 2021 by RagvaloD
Source: 2014 SPbU finals, grades 10-11 p5 v8 - Saint Petersburg State University School Olympiad
On the diagonal $BD$ of the square $ABCD$, point $P$ is selected, and on the side of $CD$, point $Q$ is selected so that the angle $\angle APQ$ is right. Line $AP$ intersects side $BC$ at point $R$. Point $S$ is selected on segment $PQ$ so that $AS = QR$. Find the angle $QSR$.
1 reply
parmenides51
Jan 22, 2021
RagvaloD
Jan 23, 2021
J
angle wanted, right angle inside a square
G H J
Reveal topic tags
geometry
angles
square
right angle
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G H BBookmark kLocked kLocked NReply
Source: 2014 SPbU finals, grades 10-11 p5 v8 - Saint Petersburg State University School Olympiad
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parmenides51
30652 posts
parmenides51
#1 h  Jan 22, 2021, 11:06 PM
Y by
On the diagonal $BD$ of the square $ABCD$, point $P$ is selected, and on the side of $CD$, point $Q$ is selected so that the angle $\angle APQ$ is right. Line $AP$ intersects side $BC$ at point $R$. Point $S$ is selected on segment $PQ$ so that $AS = QR$. Find the angle $QSR$.
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RagvaloD
4918 posts
RagvaloD
#2 h  Jan 23, 2021, 5:05 PM
Y by
$\angle DAP=180^o- \angle DQP=\angle CQP =90^o-\angle BAP=90^o-\angle BCP = \angle QCP$ so $QP=PC=PA$
So $\triangle ASP=\triangle QRP \to SP=PR \to \angle PSR=45^o \to \angle QSR =135^o$
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