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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

9 Theory of Quadratic Residues

“Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.”

– Johann Wolfgang von Goethe

9.1 Introduction

In the chapter Fermat’s little theorem, we defined quadratic congruence equation of the form ax2 + bx + c ≡ 0(mod p), p being an odd prime and a ≢ 0( mod p). There we have discoursed the solution of the quadratic congruence of the type x2 + 1 ≡ (mod p). Also, how to solve a quadratic congruence of that form, was being treated there. Following the path of solving a quadratic congruence, we need an important fact of modern number theory, known as quadratic reciprocity law, a major contribution of Gauss in 1796. After ...

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Publisher Resources

ISBN: 9781000562583