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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

4Theory of Congruences

“Number theorists are like lotus-eaters—having tasted this food they can never give it up.”

– Leopold Kronecker

4.1 Introduction

If two numbers a and b be such that the difference a−b is divisible by an integer n, then a and b are said to be “Congruent modulo n”. The number n is called the modulus and the statement “a is congruent to b(mod n)” is analytically written as

ab( modn ).

The quantity a is often said to be the base and the quantity b is called the residue or remainder. There are several types of residues. The common residue defined to be the non-negative and smaller than n while the minimal residue is b or bn, whichever is smaller than absolute terms.

Perhaps, congruence arithmetic is mostly treated ...

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Publisher Resources

ISBN: 9781000562583