Determine all possible pairs (x,y) of positive integers such that gcd(x,y)=1 and x/y + 14y/(9x) is an integer.

Prove that there are no others.

(x,y,z)= (2,3,3); for getting a sum=3

(x,y,z)= (1,3,5); (7,3,5 ) for getting a sum=5

Edited, (after seeing Charlie's post) erasing solutions with gcd not =1.

Did not fnd (14,3,5) - so actually there are 4 anwers.

*Edited on ***August 9, 2014, 2:05 pm**