SOLUTION: If N=2^1500 what is the remainder when N is divided by 13? A) 1 B) 2 C) 4 D) 12

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Question 884543: If N=2^1500 what is the remainder when N is divided by 13?
A) 1
B) 2
C) 4
D) 12
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219) About Me  (Show Source):
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
We use the theorem

2n(p-1) ≡ 1 (mod p)  where p is prime

21500 mod 13 = 2125*12 = 2125(13-1)

Using the theorem with n=125, p = 13,

Answer: 1

Edwin