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perfect number


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An integer that is equal to the sum of its positive divisors (not including itself). Thus, 6 is a perfect number, since its positive divisors (not including itself) are 1, 2 and 3, and 1+2+3=6; so too are 28 and 496, for example. At present there are over 30 known perfect numbers, all even. If 2p−1 is prime (so that it is a Mersenne prime), then 2p−1(2p−1) is perfect; moreover, these are the only even perfect numbers. It is not known if there are any odd perfect numbers; none has been found, but it has not been proved that one cannot exist.

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Perfect_numbers.html A brief history of perfect numbers.

Subjects: Mathematics.


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