I have to demonstrate this three formulae:
- $\gcd(ac,bc)=c\gcd(a,b), \forall a,b,c \in \mathbb{N}$
- $a\mid c \land b\mid c \land \gcd(a,b)=1 \implies ab\mid c$
- $\gcd(a,b,c)=xa+yb+zc, \forall a,b,c,x,y,z \in \mathbb{Z}$
and I have no idea to get started using the definition of GCD ($\gcd=\max(k\in \mathbb{N} : k\mid ac\land k\mid bc)$) or other things.
Could you help me please?