Two numbers where each one exactly equals the sum of the other's own divisors
The divisors of 220, excluding itself, are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110. Add them up. Now find the divisors of 284, excluding itself, and add those. What do you notice?
Reveal the answer
1+2+4+5+10+11+20+22+44+55+110 = 284, and the divisors of 284 (1, 2, 4, 71, 142) add up to exactly 220: each number is 'built from' the other. Known to the Pythagoreans as a symbol of friendship, 220 and 284 are the smallest amicable pair; the next pair isn't found until 1184 and 1210. Fermat, Descartes and Euler all later discovered their own amicable pairs using general formulas.