Determine all possible triplet(s) (p,q,r) of positive rational numbers such that each of p+q+r, p^-1 + q^-1 + r^-1 and p*q*r is an integer.

(1,1,1)

(3,3,3)

(2,2,1) and its permutations

I can't think of any where the rational numbers are not also integers.

Edited on June 16, 2009, 12:24 pm

Posted by Charlie on 2009-06-16 12:24:14