1. ## proof and intergers

Hi,

Does anyone know how to solve this one :

let a, b, c Z ( integer set ) with a|b and a|c , show that for any m , n Z , a|mb+nc

2. If $a|b$ then there's a $k_1 \in \mathbb{Z}$ s.t $k_1a=b$. If $a|c$ then there's a $k_2 \in \mathbb{Z}$ s.t $k_2a=c$.

For any $m,n \in \mathbb{Z}$, $mb+nc=m(k_1a)+n(k_2a)=(mk_1+nk_2)a \Rightarrow a|mb+nc.$