Question

Find least positive residue of 2^32 modulo 47

Answer 1

Please show steps

Answer 2

2^1 % 47 = 2
2^2 % 47 = 4
2^4 % 47 = 16
2^8 % 47 = 16*16 % 47 = 21
2^16 % 47 = 21*21 % 47 = 18
2^32 % 47 = 18*18 % 47 = 42

Answer 3

What are the steps you are taking. I see them but I am not exactly sure why you are taking them steps. For instance, why are are going to 2^8? Why are you choosing the exponents that you are choosing? Why 16*16/ or 21*21?

Answer 4

2^1 % 47 = 2
2^2 % 47 = 4
2^4 % 47 = 16
2^8 % 47 = (2^4 % 47)^2 % 47 = 16*16 % 47 = 21
2^16 % 47 = (2^8 % 47)^2 % 47 = 21*21 % 47 = 18
2^32 % 47 = (2^16 % 47)^2 % 47 = 18*18 % 47 = 42

Answer 5

is it safe to say that you squared each time. (2^1)^2=(2^2), (2^2)^2= 2^4 and so on

Answer 6

Yes it's safe

Answer 7

Great thank you