Problem 7. Let M = 2" – 1, where n is an odd prime. Let p...

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Problem 7. Let M = 2 – 1, where n is an odd prime. Let p be any prime factor of M. Prove that p=n·2j + 1 for some positive i

Answer 1

Answer #1

DEFINITIONS Fermats little theorem states ap-1 = 1 (mod p) if p is prime and a not divisible by p. Division algorithm Let a

consider n=p and k=j

SOLUTION Given: p is an odd prime To proof: Every divisor of the Mersenne number 2 – 1 is of the form 2kp+1 with k a nonnegat

If ged(p. 9 - 1) = 1, then ged(2P – 1,29–1 - 1) = 280d(p.4-1) - 1 = 21 -1 = 2-1 = 1. However, this is not possible as ged(2P

Prove Every divisor of the Mersenne number 2 – 1 is of the form 2kp + 1 with k a nonnegative integer. by choosing a random

Answer 2

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