Difference between revisions of "Euler's theorem"
Mathletema (talk | contribs) (Created the page as well as added an example with solution) |
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===Question=== | ===Question=== | ||
| − | Find <math>7^{18} \ | + | Find <math>7^{18} \pmod{54}</math> |
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===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 
