I have to prove this particular statement:
$\forall d \in \mathbb{N}-\{0,1\}\hspace{1em}\exists a,b,u,v \in \mathbb{Z}-\{0\}\hspace{1em}(ua+vb=d~\wedge~gcd(a,b)≠d)$
What's the best way to start off?
I always have that problem with proofs, I never know which facts can be assumed true and which require further proving.
Thanks in advance.