a.) Prove the following: Lemma. Let a and b be integers. If both a and b...

a.) Prove the following: Lemma. Let a and b be integers. If both a and b have the form 4k+1 (where k is an integer), then ab also has the form 4k+1.

b.)The lemma from part a generalizes two products of integers of the form 4k+1. State and prove the generalized lemma.

c.) Prove that any natural number of the form 4k+3 has a prime factor of the form 4k+3.

Expert Solution

Colby Messinger answered 1 year ago

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a.) Prove the following: Lemma. Let a and b be integers. If both a and b...

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