# Tagged: prime number

## Mathematics About the Number 2018

Happy New Year 2018!!

Here are several mathematical facts about the number 2018.

## 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 90

Find the largest prime number less than one million.
Let $p$ be a prime number. Suppose that the order of each element of a finite group $G$ is a power of $p$. Then prove that $G$ is a $p$-group. Namely, the order of $G$ is a power of $p$.