Problem 2: Indirect and Euclidean proofs (40 pts) For the following problems, you must use an...

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.

Expert Solution

Colby Messinger answered 2 years ago

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