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Definition 22

A perfect number is that which is equal to the sum of its own parts.

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For example, the number 28 is perfect because its parts (that is, proper divisors) 1, 2, 4, 7, and 14 sum to 28. The four smallest perfect numbers are 6, 28, 496, and 8128. In proposition IX.36 Euclid gives a construction of even perfect numbers. It is still unknown if there are any odd perfect numbers.

Book VII Introduction - Definitions 20 and 21 - Proposition 1.

© 1997
D.E.Joyce
Clark University