If u and v have different parities( one is even and one is odd), then ( a,b,c) is primitive.

Fact: If (a, b, c) is not primitive, then there exists a prime number p and natural numbers a`, b`, c` , such that a=pa`, b=pb` , c=pc`

Fact 2: if p is a prime number, and m,n are elements of N such tha p|mn , then p|m or p|n