For all integers $a$, $b$, $d$, if $d$ divides $a$, and $d$ divides $b$, then $d$ divides $(3a+2b)$ and $d$ divides $(2a+b)$. Prove the statement.
What Assumptions do I need to make at the beginning of this proof that include $(3a+2b)$ and $(2a+b)$. I can start off the proof with:
Suppose $a$, $b$, $d$ are integers and that $d$ divides $a$, and $d$ divides $b$. Then by definition of divisibility, there exist integers $c$, $k$, such that $a= dc$ and $b=dk$.
Any hint as to where to go from there?
Just write out what $3a+2b$ and $2a+b$ equal after making the substitutions $a=dc$ and $b=dk$.