Consider the following statement: For each integer a, if a = 3 (mod 8), then a...

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Consider the following statement: For each integer a, if a = 3 (mod 8), then a = 1 (mod 4). (1) Demonstrate that the result is true for a = 3, a = 11 and a = -5. (2) Prove the statement. Proof. Let a be an integer such that a = 3 (mod 8). Since a = 3 (mod 8) there exists an integer k such that a = 8k +3. Consider the following statement: For each integer a, if a = 3 (mod 8), then a = 1 (mod 4). (1) Demonstrate that the result is true for a = 3, a = 11 and a = -5. (2) Prove the statement. Proof. Let a be an integer such that a = 3 (mod 8). Since a = 3 (mod 8) there exists an integer k such that a = 8k +3.

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To demonstrate that the result is true for a 3 a 11 and a for ea... View the full answer