Question

Given 2^X mod 59 = 1. What is the value of X?

Answer 1

Hi,

Given that 2ˣ mod 59 = 1

Here, the idea is to use Fermat's little theorem,,

Fermat's Little theorem states that if p is a prime number, then for any

integer a which does not divide p, the number a^(p-1) − 1 is an integer

multiple of p. In the notation of modular arithmetic, this is expressed as

a^(p-1) mod p = 1.

Now, in the above question consider p = 59 and a = 2

Since 2 does not divide 59, Using Fermat's theorem

we can say that 2⁵⁸ mod 59 = 1

Hence, the value of X is 58.

Hope, it helped !