Consider the following statement: For each integer a, if a = 2 (mod 8), then a = 4 (mod 8). a. Demonstrate that the result is true for a = 2, a = 10 and a = -6. b. Prove the statement. Proof. Let a be an integer such that a = 2 (mod 8). Since a = 2 (mod 8) there exists an integer k such that a = 8k +2. c. Show that the converse (reverse direction) is false. That is find a counterexample for the statement: For every integer a, if a 4 (mod 8), then a = 2 (mod 8).