Clearly if (a,b) is a solution then so is (ca,cb) for any natural number c. So the only interesting solutions will be those for which a and b have no common divisor. There are two such solutions.
Spoiler:
They are (a,b) = (3,5) and (a,b) = (7,5). Now prove that there are no others.
Clearly if (a,b) is a solution then so is (ca,cb) for any natural number c. So the only interesting solutions will be those for which a and b have no common divisor. There are two such solutions.
Spoiler:
They are (a,b) = (3,5) and (a,b) = (7,5). Now prove that there are no others.