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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.

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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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Number Theory Chain!
JetFire008   61
N 3 minutes ago by JetFire008
I will post a question and someone has to answer it. Then they have to post a question and someone else will answer it and so on. We can only post questions related to Number Theory and each problem should be more difficult than the previous. Let's start!

Question 1
61 replies
JetFire008
Apr 7, 2025
JetFire008
3 minutes ago
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F.E....can you solve it?
Jackson0423   7
N 6 minutes ago by SpeedCuber7
Find all functions \( f : \mathbb{R} \to \mathbb{R} \) such that
\[ f\left(\frac{x^2 - f(x)}{f(x) - 1}\right) = x \]for all real numbers \( x \) satisfying \( f(x) \neq 1 \).
7 replies
Jackson0423
3 hours ago
SpeedCuber7
6 minutes ago
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Algebra Pure one
Jackson0423   0
21 minutes ago

Let \( x_1, x_2, \dots, x_6 \) be six distinct real numbers satisfying the following condition:

For each \( i = 1, 2, \dots, 6 \),
\[ x_i^6 + (-1)^{i+1} x_i = -x_1 x_2 x_3 x_4 x_5 x_6. \]
Find the maximum value of \( x_1 x_2 + x_3 x_4 + x_5 x_6 \).
0 replies
Jackson0423
21 minutes ago
0 replies
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IMO Genre Predictions
ohiorizzler1434   44
N 26 minutes ago by Jackson0423
Everybody, with IMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
44 replies
ohiorizzler1434
May 3, 2025
Jackson0423
26 minutes ago
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Polynomial
kellyelliee   1
N 3 hours ago by Jackson0423
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
1 reply
kellyelliee
Today at 3:57 AM
Jackson0423
3 hours ago
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Sum of digits is 18
Ecrin_eren   14
N 3 hours ago by jestrada
How many 5 digit numbers are there such that sum of its digits is 18
14 replies
Ecrin_eren
May 3, 2025
jestrada
3 hours ago
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IOQM 2022-23 P-7
lifeismathematics   2
N 4 hours ago by Adywastaken
Find the number of ordered pairs $(a,b)$ such that $a,b \in \{10,11,\cdots,29,30\}$ and
$\hspace{1cm}$ $GCD(a,b)+LCM(a,b)=a+b$.
2 replies
lifeismathematics
Oct 30, 2022
Adywastaken
4 hours ago
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Inequalities
sqing   7
N 5 hours ago by sqing
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. $
$$ a+b+3c^3\geq\sqrt{\frac{2} {3}}$$$$ a+b+2c^4\geq \frac{5} {8}$$
7 replies
sqing
Yesterday at 12:46 PM
sqing
5 hours ago
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China MO 1996 p1
math_gold_medalist28   1
N Today at 9:58 AM by MathsII-enjoy
Let ABC be a triangle with orthocentre H. The tangent lines from A to the circle with diameter BC touch this circle at P and Q. Prove that H, P and Q are collinear.
1 reply
math_gold_medalist28
May 2, 2025
MathsII-enjoy
Today at 9:58 AM
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If it is an integer then perfect square
Ecrin_eren   1
N Today at 9:36 AM by Pal702004


"Let a, b, c, d be non-zero digits, and let abcd and dcba represent four-digit numbers.

Show that if the number abcd / dcba is an integer, then that integer is a perfect square."



1 reply
Ecrin_eren
May 1, 2025
Pal702004
Today at 9:36 AM
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A Collection of Good Problems from my end
SomeonecoolLovesMaths   6
N Today at 8:53 AM by SomeonecoolLovesMaths
This is a collection of good problems and my respective attempts to solve them. I would like to encourage everyone to post their solutions to these problems, if any. This will not only help others verify theirs but also perhaps bring forward a different approach to the problem. I will constantly try to update the pool of questions.

The difficulty level of these questions vary from AMC 10 to AIME. (Although the main pool of questions were prepared as a mock test for IOQM over the years)

Problem 1

Problem 2

Problem 3

Problem 4
6 replies
SomeonecoolLovesMaths
Yesterday at 8:16 AM
SomeonecoolLovesMaths
Today at 8:53 AM
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parallelogram in a tetrahedron
vanstraelen   0
Today at 6:43 AM
Given a tetrahedron $ABCD$ and a plane $\mu$, parallel with the edges $AC$ and $BD$.
$AB \cap \mu=P$.
a) Prove: the intersection of the tetrahedron with the plane is a parallelogram.
b) If $\left|AC\right|=14,\left|BD\right|=7$ and $\frac{\left|PA\right|}{\left|PB\right|}=\frac{3}{4}$,
calculates the lenghts of the sides of this parallelogram.
0 replies
vanstraelen
Today at 6:43 AM
0 replies
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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
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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
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Number theory
MuradSafarli   1
N Apr 29, 2025 by Sadigly
Prove that for any natural number \( n \) :

\[ 1 \cdot 3 \cdot 5 \cdot \ldots \cdot (2n + 1) \mid (4n + 3)(4n + 5) \cdot \ldots \cdot (8n + 3). \]
1 reply
MuradSafarli
Apr 29, 2025
Sadigly
Apr 29, 2025
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Number theory
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number theory
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MuradSafarli
109 posts
MuradSafarli
#1 h  Apr 29, 2025, 7:39 PM
Y by
Prove that for any natural number \( n \) :

\[ 1 \cdot 3 \cdot 5 \cdot \ldots \cdot (2n + 1) \mid (4n + 3)(4n + 5) \cdot \ldots \cdot (8n + 3). \]
This post has been edited 1 time. Last edited by MuradSafarli, Apr 29, 2025, 7:41 PM
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Sadigly
159 posts
Sadigly
#3 h  Apr 29, 2025, 8:28 PM
Y by
Just try to write it like $\text{something something}\binom{8n+3}{4n+1}$
This post has been edited 1 time. Last edited by Sadigly, Apr 29, 2025, 8:32 PM
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