Amicable Numbers



“For 220 is divisible by 1 and 220 itself, with nothing left over. So 1 and 220 are factors of 220….By what else can you divide it by?”

“By 2, and 10…”

“Exactly! So let’s try writing out the factors of 220 and 284, excluding the numbers themselves, like this.”

220 : 1 2 4 5 10 11 20 22 44 55 110

142 71 4 2 1 : 284

“Add them up,” he said. “Take your time. There’s no hurry.”

220 : 1 +2 +4 +5 +10+ 11 +20 +22 +44 +55 +110 = 284

220= 142 +71+ 4 +2 1 : 284

“That’s right! The sum of the factors of 220 is 284, and the sum of the factors of 284 is 220. They’re called ‘amicable numbers’ and they’re extremely rare. Fermat and Descartes were only able to find one pair each. They’re linked to each other by some divine scheme, and how incredible that your birthday and this number on my watch should be just such a pair.”

We sat staring at the advertisement for a long time. With my finger, I traced the trail of numbers from the ones the Professor had written to the ones I’d added, and they all seem to flow together, as if we’ve been connecting up the constellations in the night sky.

Yoko Ogawa, The Housekeeper + the Professor

You see, sometimes, I’d like to think that Mathematics is nothing but a grand, complex metaphor for something else more romantic.

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