Difference between revisions of "Euler's theorem"

Revision as of 09:21, 27 August 2016

Euler's Theorem states that ${a}^{\phi(n)} \equiv 1 \quad\mod n$ , where $\phi(n)$ is Euler's Totient Theorem, and $a$ and $n$ are coprime.

Find $7^{18} \quad\mod 54$

$\phi(54) = 54*1/2*2/3 = 18$ Therefore $7^{18} \equiv {7}^{\phi(54)} \equiv \boxed{1} \quad\mod 54$