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Number Theory and its Applications
book

Number Theory and its Applications

by Satyabrota Kundu, Supriyo Mazumder
January 2022
Intermediate to advanced content levelIntermediate to advanced
366 pages
9h 15m
English
CRC Press
Content preview from Number Theory and its Applications

8 Primitive Roots

“The mathematician Pascal admires the beauty of a theorem in number theory; it’s as though he were admiring a beautiful natural phenomenon. Its marvellous, he says, what wonderful properties numbers have. It’s as though he were admiring the regularities in a kind of crystal.”

– Ludwig Wittgenstein

8.1 Introduction

In this chapter we have studied another important aspect of modular arithmetic called primitive root. To study primitive roots we have introduced the concept of order of an integer modulo k(∈ ℝ+). The order of an integer a modulo k is the least positive integer t for which at ≡ 1(mod k), where gcd(a, k) = 1. Basically for this value of k, a becomes the primitive root of k if t becomes ϕ(k). For instance 3 is a ...

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Publisher Resources

ISBN: 9781000562583