Show directly that for p a prime integer, p can be written as p=(a)^2 - d(b)^2 then d is a perfect square in Z/pZ. Hint: Are a and b elements of Z/pZ? Are a and b elements of Z/pZ*?
Show directly that for p a prime integer, p can be written as p=(a)^2 - d(b)^2 then d is a perfect square in Z/pZ. Hint: Are a and b elements of Z/pZ? Are a and b elements of Z/pZ*?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 56RE
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Show directly that for p a prime integer,
p can be written as p=(a)^2 - d(b)^2 then d is a perfect square in Z/pZ.
Hint: Are a and b elements of Z/pZ? Are a and b elements of Z/pZ*?
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