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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

7 Euler's Generalization and ϕ-function

“Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reasons to believe that it is a mystery into which the human mind will never penetrate.”

– Leonhard Euler

7.1 Introduction

Fermat’s work does not contribute much to the mathematics of his own day but creates a lasting impression on later generations of mathematics and Leonhard Euler (1707 – 1783) was the first one to appreciate its significance. Many theorems(without proof) were proclaimed by Fermat, and were later on proved by Euler with the similar arguments formulated by him.

Present chapter deals with Euler’s generalization of Fermat’s Little Theorem, depending on a function which ...

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Publisher Resources

ISBN: 9781000562583