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
If $\displaystyle a|b$ then there's a $\displaystyle k_1 \in \mathbb{Z}$ s.t $\displaystyle k_1a=b$. If $\displaystyle a|c$ then there's a $\displaystyle k_2 \in \mathbb{Z}$ s.t $\displaystyle k_2a=c$.
For any $\displaystyle m,n \in \mathbb{Z}$, $\displaystyle mb+nc=m(k_1a)+n(k_2a)=(mk_1+nk_2)a \Rightarrow a|mb+nc.$