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 c
then 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 p
which shows that , b is divisible by a.
Hence proved.