8. (25 points) Let n be a positive integer with n > 2. (a) (5 points) Prove or give a counterexample to the following st

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8 25 Points Let N Be A Positive Integer With N 2 A 5 Points Prove Or Give A Counterexample To The Following St 1 (68.56 KiB) Viewed 13 times

8. (25 points) Let n be a positive integer with n > 2. (a) (5 points) Prove or give a counterexample to the following statement: if a and b are integers such that ab 0 mod n, then either a 20 mod n or 6 0 mod n. (b) (10 ponits) Prove the following using contraposition: if a and b are integers such that 3|ab, then either 3ja or 3|b. (Hint, there are a number of similar cases that must be addressed, but you can do it efficiently). (c) (10 points) Use part (b) to prove the following statement: if a and b are integers such that ab 0 mod 3, then either a 20 mod 3 or b 0 mod 3.