Question

Let a, b, c, m and n be integers. Prove that if a|b and a|c, then
a|(bm+cn).

Answer 1

We are given the definition and theorem:

Definition: Let a and b be integers. The number a divides the number b if
there is some integer q such that aq=b. If a divides b, we write a|b, and we say that
a is a factor of b, and that b is divisible by a/

Theorem: Let a, b and c be integers. If a|b and b|c, then a|c.

Answer 2

Can you help? @ganeshie8

Answer 3

So we know that, there exists integer k such that ak = bm+cn...

I'm stuck on what to do next...

Answer 4

let a|b and a|c, then there exist k,g integers such that

b=ak
c=ag
then if there is integers m,n then :-
a|a(km+nq)
cuz a|a :)
a need not to devide (km+nq)
so...
a| (ak)m+(aq)n (right ?)
thus
a|bm+cn
done !

Answer 5

Hmm yeah this is good.

Thanks!