2.3 Euler's Theorem | 2.3 Euler's Theorem | Unit 2: Structures | Mathematics for Computer Science | Electrical Engineering and Computer Science

<Z mod n
2.3.1Modular Exponentiation Euler's Function: Video
2.3.2Euler's Totient Function
2.3.3The Ring Z: Video
2.3.4The Ring
2.3.5Z mod n
2.3.6Fermat's Little Theorem
2.3.7Euler's Theorem
>Euler's Theorem

Fermat's Little Theorem

What is \(rem(24^{78}, 79)\)?
Hint: You should not need to do any calculation!

Since 79 is prime and 24 is not a multiple of 79, Fermat's Little Theorem is applicable, and it implies that \(24^{79-1}\) is congruent to 1 modulo 79. This means that \(rem(24^{78}, 79) = 1\).