# Tagged: number theory

## Problem 446

Prove that there are infinitely many prime numbers in ONE-LINE.

## Problem 344

Let $a, b$ be relatively prime integers and let $p$ be a prime number.
Suppose that we have
$a^{2^n}+b^{2^n}\equiv 0 \pmod{p}$ for some positive integer $n$.

Then prove that $2^{n+1}$ divides $p-1$.

## Mathematics About the Number 2017

Happy New Year 2017!!

Here is the list of mathematical facts about the number 2017 that you can brag about to your friends or family as a math geek.

## Problem 219

Use Lagrange’s Theorem in the multiplicative group $(\Zmod{p})^{\times}$ to prove Fermat’s Little Theorem: if $p$ is a prime number then $a^p \equiv a \pmod p$ for all $a \in \Z$.

## Problem 90

Find the largest prime number less than one million.