Let d be a fixed positive integer greater than one Recall fr

Let d be a fixed positive integer greater than one. Recall from the Division Algorithm that a\' = a mod d if a = qd +a\', with 0 lessthanorequalto a\'

Solution

Using the division algorithm

since, a\'=a mod d and b\'=b mod d we have

a=qd+a\'

b=pd+b\'

a+b=qd+a\'+pd+b\'=(q+p)d+(a\'+b\')

Hence, a+b=a\'+b\' mod d