6

Part of 2008 Baltic Way

Problems(1)

Set of positive integers

Source: Baltic Way 2008, Problem 6

Find all finite sets of positive integers with at least two elements such that for any two numbers

a

b

a > b

) belonging to the set, the number \frac {b^2}{a \minus{} b} belongs to the set, too.

number theory unsolvednumber theoryextremal principle