How do I prove this:Let S = {x2 − y2 ∈ N : x, y ∈ Z, x2 − y2 > 127}. Prove that S has a smallest element.

Given S={x2-y2∈N: x,y∈Z, x2-y2>127} Theorem (Well ordering Principle) Every Nonempty subset of…

Answered: S = {x2 − y2 ∈ N : x, y ∈ Z, x2 − y2 >…

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S = {x2 − y2 ∈ N : x, y ∈ Z, x2 − y2 > 127}. Prove that S has a smallest element.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .

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