Difference between revisions of "Euler's theorem"

Latest revision as of 19:58, 3 August 2023

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 $7^{18} \pmod{54}$

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

@@ Line 5: / Line 5: @@
 ===Question===
-Find <math>7^{18} \pmod 5</math>
+Find <math>7^{18} \pmod{54}</math>
 ===Solution===
 <math>\phi(54) = 54*1/2*2/3 = 18</math> Therefore <math>7^{18} \equiv {7}^{\phi(54)} \equiv \boxed{1} \quad\mod 54</math>