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This answer requires a couple of basic math concepts that you may or may not remember. Here are a few quick, helpful definitions: - Dividend - a number that is being divided
- Divisor - the number by which a dividend is divided
- Aliquot - an integer that is contained an exact number of times in another number
Now, back to the problem at hand. What do the numbers 220 and 284 have in common? (Don't worry, we couldn't guess either.) They have a peculiar, friendly relationship -- a mysterious, amicable link that has fascinated mathematicians since ancient
times. If you add together all the aliquots of 220, the sum equals 284. If you do the same for 284, guess what the sum is? Right you are, it's 220! Here, watch:
Divisors of 220:
1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284
Divisors of 284:
1 + 2 + 4 + 71 + 142 = 220
Not to be confused with perfect or sociable numbers, an amicable pair is "a pair of numbers each of which equals the sum of the other's aliquot parts." Some mathematicians have assembled huge lists of amicable
pairs. Apparently, there's an infinite quantity of these numbers. Known to Pythagoras and his mystical, mathematical followers (circa 500 BC), amicable pairs were also known to early numerologists, makers of talismans and potions. Over the next couple millennia, great mathematicians like Fermat and Euler slowly, rigorously discovered additional amicable pairs. With the advent of computers, new amicable pairs were discovered with much more ease.
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