Question

If aſc and a +b = C, prove that a|b.

Answer 1

Assuming a being a divisor of c and
`a,b,c \in \mathbb{Z}`

Explanation:

We are told that
`a \mid c`

and that
`a+b =c`

which means that

`\exists k \in \mathbb{N}` so that
`c = k.a`

so we can rewrite
`a+b` as

`a+b = c = k.a`

`b = k.a-a = (k-1).a`

and as
`k \in \mathbb{N}`

We have that either

Showing that
`a \mid c`