p there are exactly o(d) numbers a such that exp, (a) =d. In particular there are exactly (p-1) primitive roots modulo p.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.2: Properties Of Division
Problem 50E
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Let p be an odd prime d | (p-1). Then in every reduced residue system mod
p there are exactly o(d) numbers a such that exp₂(a) = d. In particular there are exactly
(p-1) primitive roots modulo p.
Transcribed Image Text:Let p be an odd prime d | (p-1). Then in every reduced residue system mod p there are exactly o(d) numbers a such that exp₂(a) = d. In particular there are exactly (p-1) primitive roots modulo p.
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