Prove that if 2^n-1 is prime, then n is prime. (please write legibly)
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Suppose n is not prime. Then ∃x,y∈Z such that n=xy.
2^xy−1=(2^x)^y − 1
=(2^y−1)(2^y(x−1) + 2^y(x−2) +...+ 2^y + 1)
Since 2n−1 is divisible by 2y−1 it must be that 2n−1 is not prime. Contradiction. Thus n must be prime.
2^xy−1=(2^x)^y − 1
=(2^y−1)(2^y(x−1) + 2^y(x−2) +...+ 2^y + 1)
Since 2n−1 is divisible by 2y−1 it must be that 2n−1 is not prime. Contradiction. Thus n must be prime.
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