Kundu S., Mazumder S. Number Theory and its Applications 2022

Textbook in PDF format

Number Theory and its Applications is a textbook for students pursuing mathematics as major in undergraduate and postgraduate courses. Please note: Taylor & Francis does not sell or distribute the print book in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
Fromancienttimes,numbertheoryhasalwaysoccupiedtheunquestionedhistoricalimportanceofthesubject.NumberTheoryisbothpureandappliedandatthesametimebothclassicalandmodern.Ithasbeentheobjectiveoftheauthorsforquitesometimetowriteanaccessibleandinvitingtextbooktonumbertheory.Foremost,thepresenttextbookwillcreateaneffectiveinstrumentforbothteachingandlearning.Theauthorsaimtointegratetherichnessandbeautyofthesubjectandatthesametimethebookisfullofunexpectedusefulness.Inthepresenttext,theauthorshaveworkedhardtoassemblemanycontrastingaspectsofnumbertheoryintoonestandardtextbook.Thisbookisidealforundergraduateandpostgraduatelevelstudents.Cer-tainlevelsofmathematicalreasoning,basicalgebraandrealanalysisarere-quiredasprerequisitestostudythematerialsofourtextbook.Thistextbookisdesignedinsuchamannerthatitwillservethepurposeforawiderangeofreaders.Someefforthasbeendevotedtomakethefirstfewchapterslesschallenging,butgraduallythechaptersbecomemorechallenging.Ateachjuncture,theinstructorhastodecidehowdeeplytopursueaparticulartopicbeforemovingaheadtoanewone.
Prerequisites
Theory of Divisibility
Prime Numbers
Theory of Congruences
Fermat’s Little Theorem
Arithmetic Functions
Euler’s Generalization and φ–function
Primitive Roots
Theory of Quadratic Residues
Integers of Special Forms
Continued Fractions
Few Non-Linear Diophantine Equations
Integers as Sums of Squares
Certainpplications on Number Theory