BONUS: (5 points) Not quite so old as perfect numbers, but quite old, are the am

Question

BONUS: (5 points) Not quite so old as perfect numbers, but quite old, are the amicable numbers. These are pairs of numbers such that each is the sum of its divisors, including one, of the other. Today many pairs of these numbers are known. (Euler published at one time a list of sixty-four pairs, two of which turned out to be false.) But the ancients knew only one, a pair of numbers which they considered the symbol of perfect harmony. One member of the pair is 220. Determine the other member of this pair

Explanation / Answer

We have the pair (m,n) is said to be amicable pair of integers if the sum of the proper divisors of m excluding m should be n and vice versa. Let m=220=11.5.2.2 Therefore proper divisors of 220 are 1,2,4,5,10,11,20,22,44,55,110 and their sum is 284. Now 284=71.2.2 Therefore the proper divisors of 284 are 1,2,4,71,142 and their sum is 220. Therefore 220,284 are amicable pair. Therefore 284 is the other number of the pair.

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