If u and v are coprime, at most one of them is even.
Proof:
We will prove this via contrapositive. "If \(u\) and \(v\) are even, then they are not coprime." Let \(u=2k\), \(v=2l\) for \(k\), \(l\) in by definition of an even number. It goes as so... \(2|u\), \(2|v\)
is a common factor to both \(u\) and \(v\) so... \(gcd(u,v) \geq 2\)
Hence, they are not coprime.
Having shown the contrapositive to be true, so is our original statement.
Q.E.D.