Question

Prove that if d|m and d|n, then d|(m+n)

Answer 1

`d\mid m` means to say there is some
`k_1` such that
`m=dk_1`. Similarly,
`d\mid n` is equivalent to saying there exists
`k_2[/te]x such that [tex]n=dk_2`.

Now,
`m+n=dk_1+dk_2=d(k_1+k_2)=dk_3`, i.e. there is some
`k_3` such that
`m+n` is a multiple of
`d`, i.e.
`d\mid(m+n)`.