1. The problem statement, all variables and given/known data m and n are positive integers with m,n≥2 where [itex] m^2=kn^2 [/itex] 3. The attempt at a solution we know that all prime factors of m have an even amount , their are no prime factors that are repeated an odd number of times. The same goes for n. if k is not a perfect square then it will have an odd number of prime factors. and then when we multiply in to n it will still be an odd number, but m has only an even number, so k has to the square of an integer so both sides have even number of each prime factor.