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PERFECT NUMBERS: AN ELEMENTARY INTRODUCTION
math.dartmouth.eduPERFECT NUMBERS 5 Must all perfect numbers be of Euclid’s type? Leonard Euler, in a posthumous paper, proved that every even perfect number is of this type. Many ingenious proofs of this fact exist. Theorem 9 (Euler). If N is an even perfect number, then N can be written in the form N = 2n−1(2n −1), where 2n −1 is prime. Proof.