Prove Forall a, b, c elementof Z^+, if a|(b + c) and a|c then a|b.

Answer with explanation:If A is a positive Integer , then if A divides B , then in terms of equation it can be written as→B=A m ,where m is any integer.⇒Now, it is given that , three elements , a , b and c belong to set of Integers.a divides b+c,and  a divides cthen we have to prove that , a divides b.Proof→b+c= k a,where k is an integer , as b+c is divisible by a.→Also, c= m a, where m is an integer.Because c is divisible by a.→b+ m a= k a→b=k a - ma→b=a (k -m)Since, k and m are both integers.So , k-m will be also an integer.Let, k-m =p→b=a pwhich shows that , b is divisible by a.Hence proved.