Difference between revisions of "Euler's theorem"
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===Question=== | ===Question=== | ||
− | Find <math>7^{18} \pmod | + | Find <math>7^{18} \pmod{54}</math> |
===Solution=== | ===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> | <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> |
Latest revision as of 18:58, 3 August 2023
Contents
Theorem
Euler's Theorem states that , where is Euler's Totient Theorem, and and are coprime.
Example
Question
Find
Solution
Therefore