In: Advanced Math
Problem 2: Indirect and Euclidean proofs (40 pts) For the following problems, you must use an indirect proof technique.
(a) (10 pts) Prove indirectly that, if a 2 is a multiple of 31, then so is a. Your proof should not consist of 30 cases – this includes absolutely no implied cases using horizontal dots (· · ·) and/or vertical dots (. . .).
(b) (15 pts) Using the result of question (a), prove that √ 31 is not a rational Q using the Euclidean method.
(c) (15 pts) Using the result of question (a), prove that √ 31 is not a rational Q using the Unique Prime Factorization Theorem.