This is an unformatted preview. Please download the attached document for the or

This is an unformatted preview. Please download the attached document for the original format.Shawn Hicks California State University Fullerton Math 430 April 7 2014 Spring 2014 Solutions to Homework 7 Sums of Two Squares 1. By using Theorem 13.3 (or its corollary) prove the following: If n 3 (mod 9) or n 6 (mod 9) then n is not a sum of two squares. Theorem 13.3: Let the positive integer n be written as n = N 2 m where m is square-free. Then n can be represented as the sum of two squares if and only if m contains no prime factor of the form 4k + 3. Corollary: A positive integer n is presentable as the sum of two squares if and only if each of its prime factors of the form 4k + 3 occurs to an even power Solution. Please describe the solution in full detail here

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