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Let x, y, and z be positive integers. Suppose that x2 + y2 = z2. Prove the following. (a) if z is even then both x and y are even. (b) x and y both cannot be odd. (c) if at least one of x, y, and z is odd then z is odd.

Let x, y, and z be positive integers. Suppose that x2 + y2 = z2. Prove the following. (a) if z is even then both x and y are even. (b) x and y both cannot be odd. (c) if at least one of x, y, and z is odd then z is odd.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 13E: 13. Let Z denote the set of all integers, and let Prove that .
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Let x, y, and z be positive integers. Suppose that x2 + y2 = z2. Prove the following. (a) if z is even then both x and y are even. (b) x and y both cannot be odd. (c) if at least one of x, y, and z is odd then z is odd.
Transcribed Image Text:Let x, y, and z be positive integers. Suppose that x2 + y2 = z2. Prove the following. (a) if z is even then both x and y are even. (b) x and y both cannot be odd. (c) if at least one of x, y, and z is odd then z is odd.
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