Please show the steps. I am stuck. Solution If a|b, then there is an integer r such that ar = b. If a|c, then there is an integer s such that as = c. Examine mb + nc. We can rewrite this as m(ar) + n(as). Factor out the a to get: mb + nc = a(mr + ns) Since m, n, r, and s are integers and Z is closed under addition and multiplication, mr+ns is an integer. So we have an integer times a equalling mb + nc, and therefore a must divide mb + nc..