The original version of this story appeared in Quanta Magazine.The simplest ideas in mathematics can also be the most perplexing.Take addition. It’s a straightforward operation: One of the first ...
By January 2020, Papadimitriou had been thinking about the pigeonhole principle for 30 years. So he was surprised when a playful conversation with a frequent collaborator led them to a simple ...
Find all positive integers $n < 10^{100}$ for which simultaneously $n$ divides $2^n$, $n-1$ divides $2^n - 1$, and $n-2$ divides $2^n - 2$.Determine all solutions in non-zero integers $a$ and ...
These problems are INMO~ish level. So trying this would be a good practice for INMO!
Let $ABCD$ be a quadrilateral. Let $M,N,P,Q$ be the midpoints of sides
$AB,BC,CD,DA$. Prove that $MNPQ$ ...
Orders
Given a prime $p$, the order of an integer $a$ modulo $p$, $p\nmid a$, is the smallest positive integer $d$, such that $a^d \equiv 1
\pmod p$. This is denoted $\text{ord}_p(a) = d$.
If ...
Hello there! It has been a long time since I uploaded a post here. I recently took a class at the European Girls' Mathematical Olympiad Training Camp 2024, held at CMI. Here are a few problems ...
Book Review of Roman Adventure Activity BookThe Children’s Book Review
Created by Jen Alliston
Ages: 4-8 | 64 Pages
Publisher: Button Books (2020) | ISBN-13: ...
Book Review of The Clover CounterSponsored* | All opinions are our ownThe Children’s Book Review
What to Expect: Mystery, international espionage, chess competition, ...