Tagged: number theory
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 laterMathematics 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 laterUse Lagrange’s Theorem to Prove Fermat’s Little Theorem
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 $a \in \Z$.
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