Difference between revisions of "Euler's theorem"
Mathletema (talk | contribs) (Created the page as well as added an example with solution) |
(→Question) |
||
Line 5: | Line 5: | ||
===Question=== | ===Question=== | ||
− | Find <math>7^{18} \ | + | 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> |
Revision as of 19:35, 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