Let and ( prime factorization of and respectively . )

We know , it is obvious that if and share the same prime divisors , the product should equal as we can find a bijection linking and .

Suppose for , they don't share all the same prime divisors , let , where is the greatest common divisor of them . Now and are relatively prime and not equal to ( if so , the other must also be , then , a contradiction . )

Let and be the prime factorization of and respectively .

Consider ,

since are distinct , we must have and . and are less than but in this case they are positive integers , this leads to a contradiction .