Q13/071) Let x,y two natural numbers such that x > y, x-y=96,? and the greatest common divisor of x and y is 16. Then x= ?, and y=?

as such there is no unique solution that is there is more than one solution

now gcd(x,y ) = 16 so x = 16m, y = 16 n and gcd(m,n) = 1 and m-n = 6

so if we take m = 6k + 1, n = 6k - 5 then gcd(m,n) = 1 and we meet the critera

so x = 96 k + 16 and y = 96 k - 80 for random k

k = 1 gives 112, 16
k =2 gives 208, 112
so on

this is one set of solution and not exhaustive