Thread: find (a,b)

Hello,

find all with such that :

Originally Posted by maria18

Hello,

find all with such that :

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.

Originally Posted by Opalg

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.

you are wrong Opalg

Spoiler:

and

Maria18, how is your solution different from Opalg's?