Tagged: prime number
A One-Line Proof that there are Infinitely Many Prime Numbers
Number Theoretical Problem Proved by Group Theory. $a^{2^n}+b^{2^n}\equiv 0 \pmod{p}$ Implies $2^{n+1}|p-1$.
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 $p-1$.
Add to solve later 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.
Add to solve later A Group with a Prime Power Order Elements Has Order a Power of the Prime.
Problem 17
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 $p$.
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