- #1

cragar

- 2,552

- 3

## Homework Statement

Suppose a,b and c are integers . Prove that if a|b and a|c then a|(b+c)

## The Attempt at a Solution

Proof:

We wish to show that if a|b and a|c then a|(b+c)

Let a,b and c be integers. If a|b then there exists an integer x such that ax=b,

and if a|c then there exists an integer y such that ay=c. If a|(b+c) then there exists an integer z such that az=(b+c).

we see that b+c=ax+ay=az

a(x+y)=az=b+c

and we see that (b+c) is divisible by a.

Is this good enough?