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Question: euclids theorem about perfect numbers depends on the prime divisor...

Question details

Euclid’s theorem about perfect numbers depends on the prime divisor prop- erty, which will be proved in the next section. Assuming this for the moment, it follows that if 2 is a prime p, then the proper divisors of 2 (those unequal to 2 itself) are

1,2,22 1-1 and p,2p,2^{2}p,...,2^{n-2}p .

QUESTION

Given that the divisors of 2 are those just listed, show that 2 is

perfect when p=2^{n-1}p is prime.

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