Call a rational number r powerful if r can be expressed in the form qpk for some relatively prime positive integers p,q and some integer k>1. Let a,b,c be positive rational numbers such that abc=1. Suppose there exist positive integers x,y,z such that ax+by+cz is an integer. Prove that a,b,c are all powerful.Jeck Lim, Singapore number theoryAPMOLTE LemmaLifting the Exponent