What is 422006 mod 17 i need mathematical calculation with

What is 4^2^2006 (mod 17) ? i need mathematical calculation with step by step

Solution

if the equation is in the form of (X^Y^Z)

1. Step -1, Find a poer of 4 that will give us the remainder 1 or -1 when divided by 17

So Its 2 , 4^2 = 16 and 16%17 = -1

2. Find the remainder when 2^2006 is Modulus division by 2 , So Its 0, which means 2^2006 can be written as 2k+0

So (4)^2k and we know that 4^2 gives remainder -1 when divided by 17 ,

So The remainder is -1 i.e 16

16 is the answer.

Thanks, let me know if there is anything.