- #1

cragar

- 2,552

- 3

## Homework Statement

m and n are positive integers with m,n≥2

where [itex] m^2=kn^2 [/itex]

## 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 into 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.