Level
pending

Given that 8191 is a Mersenne prime, find the last three digits of the even perfect number $N$ that has 8191 as a factor, given that $N$ is less than 1 billion.

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Details and assumptions
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A perfect number is equal to the sum of its proper divisors (divisors excluding itself).

The answer is 336.

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No code required...Only a little computation required to know that $8191=2^{13}-1$ since it is a Mersenne prime. From Euclid's proposition:

$(2^{p-1})(2^{p}-1)$

* is an even perfect number whenever $2^{p}-1$ is prime .*So since $2^{13}-1$ is a prime $(2^{12})(2^{13}-1)$ must be an even perfect number. This number is

33550336giving us the answer336