Project B11 Page 5 of 6

A pair of natural numbers is called amicable if each is the sum of the proper divisors of the other. The ancient Greeks knew of only one pair of amicable numbers.

List the proper divisors of 220.

What is the sum of the proper divisors of 220?

List the proper divisors of 284.

What is the sum of the proper divisors of 284?

Are 220 and 284 amicable? Yes No

If 17296 is one of a pair of amicable numbers, what is the other one?

Is it possible for a perfect number to be one of an amicable pair of distinct numbers? Explain. Be sure your entire answer fits in the box shown below.

When you are satisfied with your results, print this page and continue with the next.