Suppose x,y,z are mutually coprime positive integers that solve x2+y2=z2. a) Show why exactly one of x,y and z is even b) assuming a) and that x is odd, show that z-y and z+y are coprime.
Suppose x,y,z are mutually coprime positive integers that solve x2+y2=z2. a) Show why exactly one of x,y and z is even b) assuming a) and that x is odd, show that z-y and z+y are coprime.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 46E
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Suppose x,y,z are mutually coprime positive integers that solve x2+y2=z2.
a) Show why exactly one of x,y and z is even
b) assuming a) and that x is odd, show that z-y and z+y are coprime.
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