Question

if a,b and c are integers with a divides (b+c) and a divides b, then a divides c. can someone explain how i would start.

Answer 1

subtract

Answer 2

\(a\) divides \(b+c\) means there is some \(j\) for which \(ja=b+c\)
similarly there is some \(k\) for which \(ka=b\)

Answer 3

subtract and get
\[ka-ja=c\] or \((k-j)a=c\) which is what you want