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k a June Highlights and 2025 AoPS Online Class Information
jlacosta   0
Jun 2, 2025
Congratulations to all the mathletes who competed at National MATHCOUNTS! If you missed the exciting Countdown Round, you can watch the video at this link. Are you interested in training for MATHCOUNTS or AMC 10 contests? How would you like to train for these math competitions in half the time? We have accelerated sections which meet twice per week instead of once starting on July 8th (7:30pm ET). These sections fill quickly so enroll today!

[list][*]MATHCOUNTS/AMC 8 Basics
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[*]AMC 10 Problem Series[/list]
For those interested in Olympiad level training in math, computer science, physics, and chemistry, be sure to enroll in our WOOT courses before August 19th to take advantage of early bird pricing!

Summer camps are starting this 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 a transformative 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][*]June 5th, Thursday, 7:30pm ET: Open Discussion with Ben Kornell and Andrew Sutherland, Art of Problem Solving's incoming CEO Ben Kornell and CPO Andrew Sutherland host an Ask Me Anything-style chat. Come ask your questions and get to know our incoming CEO & CPO!
[*]June 9th, Monday, 7:30pm ET, Game Jam: Operation Shuffle!, Come join us to play our second round of Operation Shuffle! If you enjoy number sense, logic, and a healthy dose of luck, this is the game for you. No specific math background is required; all are welcome.[/list]
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0 replies
jlacosta
Jun 2, 2025
0 replies
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Cyclic Quadrilateral in a Square
tobiSALT   5
N 16 minutes ago by MathLuis
Source: Cono Sur 2025 #1
Given a square $ABCD$, let $P$ be a point on the segment $BC$ and let $G$ be the intersection point of $AP$ with the diagonal $DB$. The line perpendicular to the segment $AP$ through $G$ intersects the side $CD$ at point $E$. Let $K$ be a point on the segment $GE$ such that $AK = PE$. Let $Q$ be the intersection point of the diagonal $AC$ and the segment $KP$.
Prove that the points $E, K, Q,$ and $C$ are concyclic.
5 replies
tobiSALT
Yesterday at 4:20 PM
MathLuis
16 minutes ago
J
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is there a maximal tlaxcalteca arithmetic progression of 11 elements?
parmenides51   1
N 34 minutes ago by venhancefan777
Source: Mathematics Regional Olympiad of Mexico Center Zone 2016 P5
An arithmetic sequence is a sequence of $(a_1, a_2, \dots, a_n) $ such that the difference between any two consecutive terms is the same. That is, $a_ {i + 1} -a_i = d $ for all $i \in \{1,2, \dots, n-1 \} $, where $d$ is the difference of the progression.

A sequence $(a_1, a_2, \dots, a_n) $ is tlaxcalteca if for all $i \in \{1,2, \dots, n-1 \} $, there exists $m_i $ positive integer such that $a_i = \frac {1} {m_i}$. A taxcalteca arithmetic progression $(a_1, a_2, \dots, a_n )$ is said to be maximal if $(a_1-d, a_1, a_2, \dots, a_n) $ and $(a_1, a_2, \dots, a_n, a_n + d) $ are not Tlaxcalan arithmetic progressions.

Is there a maximal tlaxcalteca arithmetic progression of $11$ elements?
1 reply
parmenides51
Nov 12, 2021
venhancefan777
34 minutes ago
J
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Easy Number Theory
math_comb01   42
N an hour ago by heheman
Source: INMO 2024/3
Let $p$ be an odd prime and $a,b,c$ be integers so that the integers $$a^{2023}+b^{2023},\quad b^{2024}+c^{2024},\quad a^{2025}+c^{2025}$$are divisible by $p$.
Prove that $p$ divides each of $a,b,c$.
$\quad$
Proposed by Navilarekallu Tejaswi
42 replies
1 viewing
math_comb01
Jan 21, 2024
heheman
an hour ago
J
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A function on a 2D grid
Rijul saini   3
N 2 hours ago by alexheinis
Source: India IMOTC 2025 Day 4 Problem 2
Does there exist a function $f:\{1,2,...,2025\}^2 \rightarrow \{1,2,...,2025\}$ such that:

$\bullet$ for any positive integer $i \leqslant 2025$, the numbers $f(i,1),f(i,2),...,f(i,2025)$ are all distinct, and
$\bullet$ for any positive integers $i \leqslant 2025$ and $j \leqslant 2024$, $f(f(i,j),f(i,j+1))=i$?

Proposed by Shantanu Nene
3 replies
Rijul saini
Jun 4, 2025
alexheinis
2 hours ago
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No more topics!
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the shortest distance between its incenter and its centroid
mr.danh   1
N Oct 22, 2016 by lmht
Source: Vietnam NMO 1996, problem 5
The triangle ABC has BC=1 and $ \angle BAC = a$. Find the shortest distance between its incenter and its centroid. Denote this shortest distance by $ f(a)$. When a varies in the interval $ (\frac {\pi}{3},\pi)$, find the maximum value of $ f(a)$.
1 reply
mr.danh
Sep 5, 2008
lmht
Oct 22, 2016
J
the shortest distance between its incenter and its centroid
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Reveal topic tags
geometry
incenter
geometry proposed
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G H BBookmark kLocked kLocked NReply
Source: Vietnam NMO 1996, problem 5
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mr.danh
635 posts
mr.danh
#1 h  Sep 5, 2008, 10:32 AM • 2 Y
Y by Adventure10, Mango247
The triangle ABC has BC=1 and $ \angle BAC = a$. Find the shortest distance between its incenter and its centroid. Denote this shortest distance by $ f(a)$. When a varies in the interval $ (\frac {\pi}{3},\pi)$, find the maximum value of $ f(a)$.
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lmht
147 posts
lmht
#2 h  Oct 22, 2016, 12:31 PM • 2 Y
Y by Adventure10, Mango247
Any solutions ?
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