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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)!

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
My Unsolved FE on R+
ZeltaQN2008   1
N 12 minutes ago by mashumaro
Source: IDK
Give $a>0$. Find all funcitions $f:\mathbb{R}^+ \rightarrow \mathbb{R}^+$ such that for all any $x,y\in (0,\infty):$
$$f(xf(y)+a)=yf(x+y+a)$$
1 reply
+1 w
ZeltaQN2008
an hour ago
mashumaro
12 minutes ago
Insects walk
Giahuytls2326   1
N 12 minutes ago by removablesingularity
Source: somewhere in the internet
A 100 × 100 chessboard is divided into unit squares. Each square has an arrow pointing up, down, left, or right. The board square is surrounded by a wall, except to the right of the top right corner square. An insect is placed in one of the squares.

Every second, the insect moves one unit in the direction of the arrow in its square. As the insect moves, the arrow of the square it just left rotates 90° clockwise.

If the specified movement cannot be performed, then the insect will not move for that second, but the arrow in the square it is standing on will still rotate. Is it possible that the insect never leaves the board?
1 reply
Giahuytls2326
May 3, 2025
removablesingularity
12 minutes ago
Inequality
MathsII-enjoy   3
N 21 minutes ago by MathsII-enjoy
A interesting problem generalized :-D
3 replies
MathsII-enjoy
Saturday at 1:59 PM
MathsII-enjoy
21 minutes ago
something...
SunnyEvan   1
N 22 minutes ago by SunnyEvan
Source: unknown
Try to prove : $$ \sum csc^{20} \frac{2^{i} \pi}{7} csc^{23} \frac{2^{j}\pi }{7} csc^{2023} \frac{2^{k} \pi}{7} $$is a rational number.
Where $ (i,j,k)=(1,2,3) $ and other permutations.
1 reply
SunnyEvan
Today at 1:13 AM
SunnyEvan
22 minutes ago
Inequalities
sqing   5
N 4 hours ago by DAVROS
Let $ a,b,c>0 $ and $ a+b\leq 16abc. $ Prove that
$$ a+b+kc^3\geq\sqrt[4]{\frac{4k} {27}}$$$$ a+b+kc^4\geq\frac{5} {8}\sqrt[5]{\frac{k} {2}}$$Where $ k>0. $
$$ a+b+3c^3\geq\sqrt{\frac{2} {3}}$$$$ a+b+2c^4\geq \frac{5} {8}$$
5 replies
sqing
Yesterday at 12:46 PM
DAVROS
4 hours ago
Polynomial
kellyelliee   0
6 hours ago
Let the polynomial $f(x)=x^2+ax+b$, where $a,b$ integers and $k$ is a positive integer. Suppose that the integers
$m,n,p$ satisfy: $f(m), f(n), f(p)$ are divisible by k. Prove that:
$(m-n)(n-p)(p-m)$ is divisible by k
0 replies
kellyelliee
6 hours ago
0 replies
Arithmetic Series and Common Differences
4everwise   6
N Today at 2:12 AM by epl1
For each positive integer $k$, let $S_k$ denote the increasing arithmetic sequence of integers whose first term is $1$ and whose common difference is $k$. For example, $S_3$ is the sequence $1,4,7,10,...$. For how many values of $k$ does $S_k$ contain the term $2005$?
6 replies
4everwise
Nov 10, 2005
epl1
Today at 2:12 AM
find number of elements in H
Darealzolt   0
Today at 1:50 AM
If \( H \) is the set of positive real solutions to the system
\[
x^3 + y^3 + z^3 = x + y + z
\]\[
x^2 + y^2 + z^2 = xyz
\]then find the number of elements in \( H \).
0 replies
Darealzolt
Today at 1:50 AM
0 replies
old problem from an open contest
Darealzolt   0
Today at 1:41 AM
Given that $a, b \in \mathbb{R}$ satisfy
\[
a + \frac{1}{a + 2015} = b - 4030 + \frac{1}{b - 2015}
\]and $|a - b| > 5000$. Determine the value of
\[
\frac{ab}{2015} - a + b.
\]
0 replies
Darealzolt
Today at 1:41 AM
0 replies
f_n(x)=\sum sin(nx)/n
Urumqi   6
N Today at 1:04 AM by Urumqi
$F_n(x)=\sum_{k=1}^{n}\frac{\sin (kx)}{k}$, prove that for all $x \in (0,\pi), F_n(x)>0$.

Thanks.
6 replies
Urumqi
Yesterday at 2:13 AM
Urumqi
Today at 1:04 AM
Looking for users and developers
derekli   9
N Today at 12:57 AM by musicalpenguin
Guys I've been working on a web app that lets you grind high school lvl math. There's AMCs, AIME, BMT, HMMT, SMT etc. Also, it's infinite practice so you can keep grinding without worrying about finding new problems. Please consider helping me out by testing and also consider joining our developer team! :P :blush:

Link: https://stellarlearning.app/competitive
9 replies
derekli
Yesterday at 12:57 AM
musicalpenguin
Today at 12:57 AM
Regular tetrahedron
vanstraelen   6
N Yesterday at 11:36 PM by Math-lover1
Given the points $O(0,0,0),A(1,0,0),B(\frac{1}{2},\frac{\sqrt{3}}{2},0)$
a) Determine the point $C$, above the xy-plane, such that the pyramid $OABC$ is a regular tetrahedron.
b) Calculate the volume.
c) Calculate the radius of the inscribed sphere and the radius of the circumscribed sphere.
6 replies
vanstraelen
Yesterday at 3:23 PM
Math-lover1
Yesterday at 11:36 PM
How many pairs
Ecrin_eren   5
N Yesterday at 10:19 PM by imbadatmath1233


Let n be a natural number and p be a prime number. How many different pairs (n, p) satisfy the equation:

p + 2^p + 3 = n^2 ?



5 replies
Ecrin_eren
May 2, 2025
imbadatmath1233
Yesterday at 10:19 PM
Name of a point on a circle
clarkculus   1
N Yesterday at 10:05 PM by martianrunner
Is there a name for the point $P'$ with respect to a circle $\Gamma$, a diameter $\ell$, and a given point $P$, such that $P'$ is the reflection of the $P$-antipode about $\ell$? Equivalently, $P'$ is the the other intersection of $\Gamma$ and the line through $P$ parallel to $\ell$.
1 reply
clarkculus
Yesterday at 9:45 PM
martianrunner
Yesterday at 10:05 PM
Funny function that there isn't exist
ItzsleepyXD   5
N Apr 26, 2025 by Hamzaachak
Source: Own, Modified from old problem
Determine all functions $f\colon\mathbb{Z}_{>0}\to\mathbb{Z}_{>0}$ such that, for all positive integers $m$ and $n$,
$$ m^{\phi(n)}+n^{\phi(m)} \mid f(m)^n + f(n)^m$$
5 replies
ItzsleepyXD
Apr 10, 2025
Hamzaachak
Apr 26, 2025
Funny function that there isn't exist
G H J
Source: Own, Modified from old problem
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ItzsleepyXD
130 posts
#1
Y by
Determine all functions $f\colon\mathbb{Z}_{>0}\to\mathbb{Z}_{>0}$ such that, for all positive integers $m$ and $n$,
$$ m^{\phi(n)}+n^{\phi(m)} \mid f(m)^n + f(n)^m$$
Z K Y
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ItzsleepyXD
130 posts
#2
Y by
Bump....
Z K Y
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EvansGressfield
3 posts
#3
Y by
any idea?
Z K Y
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Rayanelba
14 posts
#4
Y by
This problem is very hard pls share some hints
Z K Y
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Hamzaachak
61 posts
#5
Y by
No such function exist
Z K Y
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Hamzaachak
61 posts
#6 • 1 Y
Y by ItzsleepyXD
Hamzaachak wrote:
No such function exist

Small hint : try to prove f(2)=0
Z K Y
N Quick Reply
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