For some reason I'm stuck on this.

For proof by contraposition:

For all integers a,b,c a | b+c --> ~(a | b) or (a | c).

Suppose a | b+c

b+c=a*k for some integer k

...

I can't figure out exactly where to go from here.

By contradiction:

suppose there exists integers a,b,c such that a | b and ~( a | c) and a | b+c

b+c=a*k for some integer k

b=a*P for some integer P

aP+c=ak

p=(ak-c)/a

p=k-c/a

?

...

I feel like this should be really easy, but I can't seam to figure it out for the moment. Any help would be appreciated.