(a) Calculate 2^5 mod 29, 2^7 mod 29 & 2^14 mod 29. Deduce from your answers the remainder when 2^1000/29?

Question

(b) find the orders and iverse of [2] base 23 and [3] basw 23 in Z/23?

(c)Using any theorems you wish (e.g fermat's, euler's or the CRT) find the remainder in the range 0 - 99 when 7^(8^9) is divided by 100.

Answer 1

I have a question too? Where is the difficulty for you?

P.S. Seriously I wanted to know!

Anyway the easiest first. 7^4 = 2401. So 7^ N = 100 a + 1 if N is a multiple of 4. Leave Fermat and Euler alone...