Math Help on Integers and Proofs!?

Assume 13a+b-5c=0 where a, b, c are integers. Show that if n≠0 is an integers such that n | a and n | c, then n | b.


Rewrite as b = 5c - 13a. Since it is said that the RHS is divisible by n, then the LHS must also be divisible by n. Done! Or, it is said that a = na' and c = nc' for some integers a' & c'. Thus b = 5c - 13a = 5nc' - 13na' = n(5c' - 13a'). IOW, n is a factor of b. n | b.