I need some hints how to proof something like the following:

Let $a,b \in \mathbb{Z}$ with $a,b \not= 0$ and let $\gcd(a,b)=d$.

(1) For any $m,n\in \mathbb{Z}$ we have $d \mid ma+nb$.

(2) There exist $t,r \in \mathbb{Z}$ so that $d = ta + rb$. 

Thank you very much for any help ;)