Sunday, May 01, 2005

Friendly Numbers

Pythagoras considered 220 and 284 to be friendly (or amicable). He even wrote: "[A friend] is the other I, such as are 220 and 284". Aristotle also used the notion of friendly numbers to characterize friendship (in his work "Ethics"). So what makes the numbers 220 and 284 so special? Their property is that each is equal to the sum of the other's proper divisors. The proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110, and they sum up to 284; the proper divisors of 284 are 1, 2, 4, 71, and 142, and they sum up to 220.

Itt olvashato Ibn Qurra Ibrahim friendly numbers kereso algoritumusa.