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(i+j)/(i,j) belongs to s

Source: APMO 2004

April 8, 2006

inductiongreatest common divisornumber theory unsolvednumber theory

Problem Statement

Determine all finite nonempty sets

S

of positive integers satisfying {i+j\over (i,j)}\qquad\mbox{is an element of S for all i,j in S}, where

(i,j)

is the greatest common divisor of

i

and

j