Fill in the blanks in the following proof that for all integers a and b, if a | b then a | (−b).
Suppose a and b are any integers such that (a). By definition of divisibility, there exists an integer r such that (b) By substitution.
−b = −ar = a(−r).
Let t = (c) Then t is an integer because t = (−1)• r, and both −1 and r are integers. Thus, by substitution, −b = at, where t is an integer, and so by definition of divisibility, (d), as was to be shown.
Given result is, for all integers