what is the remainder when 314162 is divided by 163 please s

what is the remainder when 314^162 is divided by 163. please show work

Solution

As per Fermat\'s theorem , the following is true

a^(p-1)/p = 1, if p is a prime number.

In the given equation, 314^162/163, the condition of Fermat\'s theorem get satisfied i.e.

a=314

p=163, which is a prime number

p-1=162

thus we have

314^162/163 = 1

therefore the remainder of the given problem i.e. 314^162/163 is 1.