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4 Number Theory I: Prime Numbers - Penn Math
www2.math.upenn.edu3. Perfect Numbers Every natural number has a set of divisors, the numbers which can evenly divide the number. For example, the natural numbers 1,2,3,4,6, and 12 all divide the number 12 itself. The number 33 has fewer divisors, which are 1, 3, 11, and 33 itself. For each number n, let’s consider the set Dn of positive integers that
PERFECT NUMBERS: AN ELEMENTARY INTRODUCTION
math.dartmouth.eduOne would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery—and more totally useless—than the perfect numbers. —Martin Gardner [2] The number 6 is unique in that 6 = 1+2+3, where 1, 2, and 3 are all of the proper divisors of 6.