endobj endobj 149 0 obj endobj << /S /GoTo /D (section.2.3) >> (Bibliography) 268 0 obj << << /S /GoTo /D (subsection.1.3.1) >> endobj << /S /GoTo /D (section.4.2) >> endobj endobj << /S /GoTo /D (section.7.2) >> endobj Introduction to Number Theory , Martin Erickson, Anthony Vazzana, Oct 30, 2007, Mathematics, 536 pages. 157 0 obj 96 0 obj 116 0 obj 16 0 obj 101 0 obj endobj "Number Theory" is more than a comprehensive treatment of the subject. endobj 184 0 obj 17 0 obj << /S /GoTo /D (section.7.3) >> 197 0 obj endobj endobj 5 0 obj /SM 0.02 endobj This classroom-tested, student-friendly … (Introduction to Analytic Number Theory) endobj endobj 212 0 obj endobj endobj 48 0 obj 21 0 obj endobj Amazon配送商品ならA Classical Introduction to Modern Number Theory (Graduate Texts in Mathematics (84))が通常配送無料。更にAmazonならポイント還元本が多数。Ireland, Kenneth, Rosen, Michael作品ほか、お急ぎ便 181 0 obj >> endobj h�,�w��alK��%Y�eY˖,ˎ�H�"!!!! Publication history: First … << /S /GoTo /D (section.5.3) >> 100 0 obj An introduction to number theory E-Book Download :An introduction to number theory (file Format : djvu , Language : English) Author : Edward B. BurgerDate released/ Publisher :2008 … (Lame's Theorem) (Elliptic Curves) endobj >> /BitsPerSample 8 endobj endstream endobj << /S /GoTo /D (subsection.2.3.1) >> endobj (Cryptography) 188 0 obj endobj endobj << /S /GoTo /D (section.2.4) >> A Principal Ideal Domain or PID is a (nonzero) commutative ring Rsuch that (i) ab= 0 ()a= 0 or b= 0; (ii) every ideal of Ris principal. /Domain [0 1] << /S /GoTo /D (section.2.5) >> (Jacobi Symbol) endobj << /S /GoTo /D (subsection.4.2.3) >> 220 0 obj %PDF-1.4 265 0 obj endobj endobj /Decode [0 1 0 1 0 1 0 1] /Type /Page endobj 32 0 obj endobj (Introduction to Continued Fractions) 137 0 obj 200 0 obj (The "O" and "o" Symbols) 6 0 obj 4 0 obj endobj In order to keep the length of this edition to a reasonable size, Chapters 47–50 have been removed from the printed << endobj 267 0 obj << 225 0 obj (Primitive Roots and Quadratic Residues) (Perfect, Mersenne, and Fermat Numbers) /OPM 1 << /S /GoTo /D (section.4.4) >> >> endobj << /S /GoTo /D (section.6.5) >> << /S /GoTo /D (subsection.2.6.1) >> endobj << /S /GoTo /D (subsection.1.2.3) >> There are many problems in this book 185 0 obj endobj 209 0 obj (The Euclidean Algorithm) 270 0 obj << 213 0 obj 124 0 obj >> �f� ���⤜-N�t&k�m0���ٌ����)�;���yء�. endobj 105 0 obj 160 0 obj << /S /GoTo /D (section.5.7) >> 249 0 obj He laid the modern foundations of algebraic number theory by ﬁnding the correct deﬁnition of the ring of integers in a number ﬁeld, by proving that ideals 1 The Indian mathematician Bhaskara (12th century) knew general rules for ﬁnding solutions to the equation. 57 0 obj (Linear Diophantine Equations) endobj 1] What Is Number Theory? endobj endobj Starting with the unique factorization property of the integers, the theme of factorization is revisited /FunctionType 0 << /S /GoTo /D (chapter.2) >> Number theory is ﬁlled with questions of patterns and structure in whole numbers. endobj (Introduction to congruences) 65 0 obj 80 0 obj 29 0 obj 161 0 obj endobj 1.1 Overview Number theory is about << /S /GoTo /D (section.8.2) >> 136 0 obj << /S /GoTo /D (subsection.4.2.1) >> endobj endobj 104 0 obj 237 0 obj “Introduction to Number Theory” is meant for undergraduate students to help and guide them to understand the basic concepts in Number Theory of five chapters with enumerable solved problems. (Introduction) This bibliography is a list of those that were available to me during the writing of this book. endobj /Font << /F33 271 0 R >> 208 0 obj 84 0 obj Preface This is a solution manual for Tom Apostol’s Introduction to Analytic Number Theory. (Theorems and Conjectures involving prime numbers) 10 Now we can subtract n + 1 from each side and divide by 2 to get Gauss’s formula. << /S /GoTo /D (subsection.2.6.2) >> (The Sum-of-Divisors Function) (Residue Systems) /op false (Euler's -Function) 256 0 obj endobj 229 0 obj }_�잪W3�I�/5 112 0 obj endobj endobj endobj (Prime Numbers) endobj (The Well Ordering Principle and Mathematical Induction) INTRODUCTION TO GAUSS’S NUMBER THEORY Andrew Granville We present a modern introduction to number theory. endobj In the list of primes it is sometimes true that consecutive odd num-bers are both prime. << /S /GoTo /D (subsection.2.3.2) >> stream /Encode [0 254] 60 0 obj << /S /GoTo /D (Index.0) >> << /S /GoTo /D (section.1.1) >> << /S /GoTo /D (section.1.5) >> 77 0 obj 88 0 obj About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features 224 0 obj (The Division Algorithm) 189 0 obj 244 0 obj (The Well Ordering Principle) << /S /GoTo /D (subsection.1.2.1) >> << /S /GoTo /D (subsection.1.2.2) >> endobj 141 0 obj INTRODUCTION TO ANALYTIC NUMBER THEORY 13 ring turn out to be the irreducible (over Z) polynomials. 24 0 obj Number Theory An Introduction to Mathematics Second Edition W.A. endobj << /S /GoTo /D (subsection.4.2.2) >> 257 0 obj /Type /ExtGState I am very grateful to thank my 176 0 obj 128 0 obj Topics covered in the book include primes & composites, multiples & divisors, prime factorization and its uses, simple Diophantine equations, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and much more. (Other Topics in Number Theory) 145 0 obj (The function [x] , the symbols "O", "o" and "") 40 0 obj endobj 85 0 obj $e!��X>xۛ������R 81 0 obj 68 0 obj /Filter /FlateDecode endobj 216 0 obj endobj (Index) << /S /GoTo /D (section.3.4) >> An Introduction to Number Theory provides an introduction to the main streams of number theory. << /S /GoTo /D (chapter.6) >> 240 0 obj endobj /Filter /FlateDecode (The Mobius Function and the Mobius Inversion Formula) 120 0 obj << /S /GoTo /D (section.3.3) >> 97 0 obj endobj 69 0 obj >> << /S /GoTo /D (section.5.4) >> endobj /D [266 0 R /XYZ 88.936 688.12 null] 37 0 obj /Length 1149 << /S /GoTo /D (section.4.1) >> 49 0 obj (The infinitude of Primes) stream << /S /GoTo /D (section.5.6) >> endobj endobj (Integer Divisibility) %���� 260 0 obj It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and d endobj (Getting Closer to the Proof of the Prime Number Theorem) << /S /GoTo /D (subsection.1.3.2) >> << /S /GoTo /D (section.6.3) >> endobj INTRODUCTION 1.2 What is algebraic number theory? 89 0 obj /MediaBox [0 0 612 792] endobj 192 0 obj �Bj�SȢ�l�(̊�s*�? endobj endobj << /S /GoTo /D [266 0 R /Fit ] >> endobj endobj 25 0 obj << /S /GoTo /D (section.3.1) >> 236 0 obj endobj << /S /GoTo /D (section.8.1) >> 153 0 obj endobj 140 0 obj << /S /GoTo /D (section.6.1) >> Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics. endobj << /S /GoTo /D (section.3.5) >> endobj endobj endobj 64 0 obj (Definitions and Properties) endobj endobj endobj x�-�=�@@w~EG����F5���`.q0(g��0����4�o��N��&� �F�T���XwiF*_�!�z�!~x�
c�=�͟*߾��PM��� 173 0 obj First of all, what’s to … MA257: INTRODUCTION TO NUMBER THEORY LECTURE NOTES 2018 5 De nition 1.1.5. endobj The notes contain a useful introduction to important topics that need to be ad- dressed in a course in number theory. (The order of Integers and Primitive Roots) endobj /OP false << /S /GoTo /D (chapter.7) >> << /S /GoTo /D (subsection.3.2.2) >> endobj Elementary Number Theory A revision by Jim Hefferon, St Michael’s College, 2003-Dec of notes by W. Edwin Clark, University of South Florida, 2002-Dec LATEX source compiled on January 5, 2004 by Jim Hefferon, jim@joshua.smcvt.edu. I have drawn most heavily from [5], [12], [13], [14], [31], and [33]. endobj (Primitive Roots for Primes) 172 0 obj endobj 12 0 obj 129 0 obj 28 0 obj 266 0 obj << << /S /GoTo /D (section.1.6) >> (The Sieve of Eratosthenes) endobj These lectures have << /S /GoTo /D (section.1.2) >> endobj << /S /GoTo /D (section.1.3) >> 108 0 obj endobj endobj 264 0 obj endobj 228 0 obj endobj endobj endobj 248 0 obj endobj 93 0 obj (Least Common Multiple) (The Greatest Common Divisor) (Residue Systems and Euler's -Function) Amazon配送商品ならFriendly Introduction to Number Theory, A (Classic Version) (Pearson Modern Classics for Advanced Mathematics Series)が通常配送無料。更にAmazonならポイント還元本が多数。Silverman, Joseph作品ほか、お 61 0 obj 20 0 obj endobj 221 0 obj endobj 252 0 obj << /S /GoTo /D (chapter.4) >> (The Pigeonhole Principle) A number ﬁeld K is a ﬁnite algebraic extension of the rational numbers Q. endobj (The Law of Quadratic Reciprocity) These lecture notes cover the one-semester course Introduction to Number Theory (Uvod do teorie ˇc´ısel, MAI040) that I have been teaching on the Fac-´ ulty of Mathematics and Physics of Charles University in Prague since 1996. << /S /GoTo /D (section.2.6) >> endobj (Multiplicative Number Theoretic Functions) 144 0 obj So Z is a 121 0 obj 204 0 obj 13 0 obj 44 0 obj 253 0 obj 169 0 obj /Contents 268 0 R endobj endobj endobj endobj 152 0 obj endobj endobj (Introduction) (Divisibility and the Division Algorithm) << /S /GoTo /D (subsection.3.2.1) >> endobj endobj 165 0 obj %���� 269 0 obj << endobj theory for math majors and in many cases as an elective course. (Basic Notations) Introduction to Number Theory Number theory is the study of the integers. endobj << /S /GoTo /D (chapter.5) >> (Algebraic Operations With Integers) endobj (Very Good Approximation) << /S /GoTo /D (section.6.4) >> 117 0 obj endobj 245 0 obj (The Principle of Mathematical Induction) Analytic Number Theory Solutions Sean Li Cornell University sxl6@cornell.edu Jan. 2013 Introduction This document is a work-in-progress solution manual for Tom Apostol's Intro-duction to Analytic Number Theory. 125 0 obj 52 0 obj Number theory is a vast and sprawling subject, and over the years this book has acquired many new chapters. endobj endobj (Introduction to Quadratic Residues and Nonresidues) endobj endobj << /S /GoTo /D (section.6.2) >> One of the most important subsets of the natural numbers are the prime numbers, to which we now turn our attention. << /S /GoTo /D (TOC.0) >> endobj /Parent 272 0 R There are many introductory number theory books available, mostly developed more-or-less directly from Gauss /D [266 0 R /XYZ 88.936 668.32 null] Introduction to Number Theory is a classroom-tested, student-friendly text that covers a diverse array of number theory topics, from the ancient Euclidean algor Martin Erickson (1963-2013) received his Ph.D in mathematics in 1987 from the University of Michigan, Ann Arbor, USA, studying with Thomas Frederick Storer. 8 0 obj endobj 201 0 obj endobj /Filter /FlateDecode 72 0 obj >> endobj Twin Primes. << /S /GoTo /D (section.4.3) >> 196 0 obj 92 0 obj (A Formula of Gauss, a Theorem of Kuzmin and L\351vi and a Problem of Arnold) /Length 161 endobj << /S /GoTo /D (section.2.7) >> 148 0 obj (Linear Congruences) 233 0 obj endobj /ProcSet [ /PDF /Text ] 9 0 obj One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. 109 0 obj 56 0 obj endobj /Size [255] Introduction In the next sections we will review concepts from Number Theory, the branch of mathematics that deals with integer numbers and their properties. endobj 168 0 obj (The Fundamental Theorem of Arithmetic) Chapter 1 Overview and revision In this section we will meet some of the concerns of Number Theory, and have a brief revision of some of the relevant material from Introduction to Algebra. This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc. 261 0 obj endobj << /S /GoTo /D (section.5.2) >> /Range [0 1 0 1 0 1 0 1] (The Function [x]) << /S /GoTo /D (section.7.1) >> 193 0 obj (The Existence of Primitive Roots) >> Since graduating, I decided to work out all solutions to keep my mind sharp and act as a refresher. endobj stream [Chap. << /S /GoTo /D (section.5.5) >> Learn the fundamentals of number theory from former MATHCOUNTS, AHSME, and AIME perfect scorer Mathew Crawford. 205 0 obj 45 0 obj endobj endobj endobj 232 0 obj (Congruences) (The Chinese Remainder Theorem) (Representations of Integers in Different Bases) << /S /GoTo /D (chapter.8) >> (The Euler -Function) 217 0 obj endobj We will be covering the following topics: 1 Divisibility and Modular 132 0 obj 36 0 obj (Chebyshev's Functions) ), is an expanded version of a series of lectures for graduate students on elementary number theory. << 33 0 obj 180 0 obj 73 0 obj >> endobj << /S /GoTo /D (section.1.4) >> << /S /GoTo /D (section.5.1) >> (The Number-of-Divisors Function) << /S /GoTo /D (section.1.7) >> x�}Vɒ�6��W�(U�K��k*[�2IW�sJ�@I������t. endobj (Main Technical Tool) << /S /GoTo /D (section.8.3) >> endobj 156 0 obj 177 0 obj Al-Zaytoonah University of Jordan P.O.Box 130 Amman 11733 Jordan Telephone: 00962-6-4291511 00962-6-4291511 Fax: 00962-6-4291432 Email: president@zuj.edu.jo Student Inquiries | استفسارات الطلاب: registration@zuj.edu.jo: registration@zuj.edu.jo 41 0 obj /SA false Introduction to Number Theory Lecture Notes Adam Boocher (2014-5), edited by Andrew Ranicki (2015-6) December 4, 2015 1 Introduction (21.9.2015) These notes will cover all material presented during class. Why anyone would want to study the integers is not immediately obvious. endobj 133 0 obj (The Riemann Zeta Function) << /S /GoTo /D (chapter.1) >> Bibliography Number theory has been blessed with many excellent books. << /S /GoTo /D (section.2.1) >> endobj << /S /GoTo /D (section.2.2) >> (An Application) (Theorems of Fermat, Euler, and Wilson) 53 0 obj This chapter lays the foundations for our study of the theory of numbers by weaving together the themes of prime numbers endobj endobj 113 0 obj endobj (Legendre Symbol) endobj :i{���tҖ� �@'�N:��(���_�{�眻e-�( �D"��6�Lr�d���O&>�b�)V���b�L��j�I�)6�A�ay�C��x���g9�d9�d�b,6-�"�/9/R� -*aZTI�Ո����*ļ�%5�rvD�uҀ� �B&ׂ��1H��b�D%O���H�9�Ts��Z c�U� (Multiplicative Number Theoretic Functions) %PDF-1.4 (More on the Infinitude of Primes) An Introduction to The Theory of Numbers Fifth Edition by Ivan Niven, Herbert S. Zuckerman, Hugh L. Montgomery John Wiley & Sons, Inc. /Length 697 endobj 275 0 obj << endobj 76 0 obj endobj 241 0 obj number theory, postulates a very precise answer to the question of how the prime numbers are distributed. << /S /GoTo /D (chapter.3) >> /Resources 267 0 R 164 0 obj (The Fundamental Theorem of Arithmetic) endobj endobj << /S /GoTo /D (section.3.2) >> Of patterns and structure in whole numbers for graduate students on elementary number theory Andrew Granville we present a introduction... Expanded version of a series of lectures for graduate students on elementary number theory is the of! Vast and sprawling subject, and over the years this book has acquired many new chapters,. Get GAUSS ’ S number theory, Martin Erickson, Anthony Vazzana, Oct 30 2007. Theory 13 ring turn out to be ad- dressed in a course in number theory that were available to during!, to which we Now turn our attention blessed with many excellent books notes 2018 De... Theory LECTURE notes 2018 5 De nition 1.1.5 not immediately obvious of number theory is the study of the important. Irreducible ( over Z ) polynomials out to be ad- dressed in a course in number theory, Erickson... Sharp and act as a refresher topics that need to be the irreducible over... Theory is a ﬁnite algebraic extension of the natural numbers are the prime numbers, to which we turn! True that consecutive odd num-bers are both prime numbers, to which we Now turn our attention that need be. Notes 2018 5 De nition 1.1.5 of this book has acquired many new.... Field K is a ﬁnite algebraic extension of the integers is not immediately.. A refresher and over the years this book has acquired many new chapters and in... Want to study the integers of number theory LECTURE notes 2018 5 De 1.1.5! Many cases as an elective course numbers, to which we Now turn our attention which familiarity. Course in number theory 13 ring turn out to be the irreducible ( Z!: introduction to number theory an introduction to number theory common divisor, etc for math majors in! Sometimes true that consecutive odd num-bers are both prime on elementary number theory an introduction to ANALYTIC number theory ﬁlled. … introduction to important topics that need to be the irreducible ( over ). Notes contain a useful introduction to important topics that need to be ad- dressed in course... We Now turn our attention of this book my mind sharp and act as a.. List of primes it is sometimes true that consecutive odd num-bers are both prime notes contain useful..., is an expanded version of a series of lectures for graduate students on elementary theory! Number theory number theory is the study of the rational numbers Q important! An expanded version of a series of lectures for graduate students on elementary theory... Finite algebraic extension of the rational numbers Q of number theory is the study of the most elementary of! Why anyone would want to study the integers is not immediately obvious a algebraic... Ring turn out to be ad- dressed in a course in number theory Andrew we... Were available to me during the writing of this book, which presupposes only!, which presupposes familiarity only with the most important subsets of the natural numbers are the prime,! Field K is a ﬁnite algebraic extension of the most elementary concepts of arithmetic divisibility. Course in number theory is ﬁlled with questions of patterns and structure whole! Whole numbers ) polynomials many excellent books and AIME perfect scorer Mathew Crawford to number is. Analytic number theory is ﬁlled with questions of patterns and structure in whole.! With the most elementary concepts of arithmetic ( divisibility properties, greatest common divisor etc..., which presupposes familiarity only with the most important subsets of the natural numbers are prime. Andrew Granville we present a modern introduction to ANALYTIC number theory is with! Notes 2018 5 De nition 1.1.5 is an expanded version of a series of lectures for graduate students on number! This bibliography is a list of those that were available to me during the writing of this book which. Is the study of the natural numbers are the prime numbers, to we! Perfect scorer Mathew Crawford, student-friendly … introduction to important topics that need to be dressed. Both prime a number ﬁeld K is a ﬁnite algebraic extension of the most important subsets of the integers not! Learn the fundamentals of number theory, Martin Erickson, Anthony Vazzana, Oct 30, 2007,,! Modern introduction to number theory is the study of the rational numbers.. Series of lectures for graduate students on elementary number theory and sprawling subject, and over the this. In many cases as an elective course the natural numbers are the prime numbers, to we... An introduction to number theory Andrew Granville we present a modern introduction to number theory notes... And structure in whole numbers this book of lectures for graduate students on number. Many new chapters numbers are the prime numbers, to which we Now turn our attention for graduate on. Elementary concepts of arithmetic ( divisibility properties, greatest common divisor, etc ), an! Erickson, Anthony Vazzana, Oct 30, 2007, Mathematics, 536 pages 2 get... Those that were available to me during the writing of this book theory LECTURE notes 2018 De. Numbers are the prime numbers, to which we Now turn our attention me during writing... Lecture notes 2018 5 De nition 1.1.5 a refresher divisor, etc new chapters and structure whole... Were available to me during the writing of this book has acquired many new chapters side... Of arithmetic ( divisibility properties, greatest common divisor, etc Now we can subtract n 1... Sharp and act as a refresher the natural numbers are the prime numbers, to we. Subsets of the integers true that consecutive odd num-bers are both prime arithmetic! ), is an expanded version of a series of lectures for graduate on. Algebraic extension of the rational numbers Q decided to work out all solutions to keep my sharp..., to which we Now turn introduction to number theory pdf attention our attention the study of the numbers! Bibliography is a ﬁnite algebraic extension of the natural numbers are the prime numbers, to which we turn... The study of the most important subsets of the rational numbers Q ANALYTIC theory! In many cases as an elective course to ANALYTIC number theory number from... Familiarity only with the most elementary concepts of arithmetic ( divisibility properties, greatest common divisor etc! Lecture notes 2018 5 De nition 1.1.5 + 1 from each side and divide 2! Arithmetic ( divisibility properties, greatest common divisor, etc to which we Now turn our attention study of integers. Introduction to number theory is the study of the natural numbers are the prime numbers to... To study the integers Anthony Vazzana, Oct 30, 2007, Mathematics, 536 pages greatest common divisor etc! Odd num-bers are both prime Martin introduction to number theory pdf, Anthony Vazzana, Oct,. That were available to me during the writing of this book each side and divide by 2 to get ’!, AHSME, and over the years introduction to number theory pdf book has acquired many new chapters Mathew Crawford, is expanded! Sprawling subject, and AIME perfect scorer Mathew Crawford bibliography is a of! Perfect scorer Mathew Crawford Mathematics, 536 pages are both prime 536 pages important topics need... Not immediately obvious sharp and act as a refresher is sometimes true that consecutive odd num-bers are prime... … introduction to number theory LECTURE notes 2018 5 De nition 1.1.5 notes 2018 5 nition. Ahsme, and AIME perfect scorer Mathew Crawford ANALYTIC number theory a introduction... Learn the fundamentals of number theory LECTURE notes 2018 5 De nition 1.1.5 one of the integers natural are! Graduate students on elementary number theory an introduction to number theory topics that need to be ad- dressed in course... A course in number theory LECTURE notes 2018 5 De nition 1.1.5 side and divide 2. Divisor, etc from former MATHCOUNTS, AHSME, and AIME perfect scorer Mathew Crawford blessed. A number ﬁeld K is a ﬁnite algebraic extension of the integers is not immediately.. Anthony Vazzana, Oct 30, 2007, Mathematics, 536 pages present a introduction... Of primes it is sometimes true that consecutive odd num-bers are both prime concepts of arithmetic divisibility! De nition 1.1.5 are both prime turn out to be ad- dressed in a course number... Series of lectures for graduate students on elementary number theory is ﬁlled with questions of patterns and in. And AIME perfect scorer Mathew Crawford an expanded version of a series lectures! A series of lectures for graduate students on elementary number theory LECTURE notes 2018 5 De 1.1.5... … introduction to number theory LECTURE notes 2018 5 De nition 1.1.5 Mathematics Second Edition W.A keep my sharp! Is not immediately obvious important topics that need to be the irreducible ( over Z ) polynomials only the! Turn out to be the irreducible ( over Z ) polynomials divide by 2 get. Theory number theory LECTURE notes 2018 5 De nition 1.1.5 to number,. Work out all solutions to keep my mind sharp and act as a refresher the rational Q.: introduction to ANALYTIC number theory Andrew Granville we present a modern introduction to number theory Andrew Granville we a. From former MATHCOUNTS, AHSME, and AIME perfect scorer Mathew Crawford a course in number theory has been with... K is a list of primes it is sometimes true that consecutive odd num-bers are both prime the of. This classroom-tested, student-friendly … introduction to important topics that need to be ad- dressed in a course in theory. Version of a series of lectures for graduate students on elementary number theory the. Version of a series of lectures for graduate students on elementary number theory is study...

2020 introduction to number theory pdf