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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

5 Fermat's Little Theorem

“Perhaps, posterity will thank me for having shown that the ancients did not know anything.”

– Pierre De Fermat

5.1 Introduction

The famous French Mathematician Pierre de Fermat first wrote what would become his “Little Theorem” in 1640. It states that for any prime number p and any integer a the expression (ap − a) is divisible by p as long as p does not divide a(the pair are relatively prime). Although a number n that does not divide an − a for some a must be a composite number but the converse is not necessarily true. An example, in the later section of the chapter, will justify the above argument. Thus, Fermat’s theorem gives a test that is necessary but not sufficient for primality. Also the theorem is applicable ...

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Publisher Resources

ISBN: 9781000562583