{"product_id":"2940016797304","title":"The Theory of Math","description":"The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The arrangement of the material is as follows:\u003cbr\u003e\u003cbr\u003eThe first five chapters are devoted to the development of those elements which are essential to any study of the subject. The sixth and last chapter is intended to give the reader some indication of the direction of further study with a brief account of the nature of the material in each of the topics suggested. The treatment throughout is made as brief as is possible consistent with clearness and is confined entirely to fundamental matters. This is done because it is believed that in this way the book may best be made to serve its purpose as an introduction to the theory of numbers.\u003cbr\u003e\u003cbr\u003eNumerous problems are supplied throughout the text. These have been selected with great care so as to serve as excellent exercises for the student's introductory training in the methods of number theory and to afford at the same time a further collection of useful results. The exercises marked with a star are more difficult than the others; they will doubtless appeal to the best students.\u003cbr\u003e\u003cbr\u003eFinally, I should add that this book is made up from the material used by me in lectures in Indiana University during the past two years; and the selection of matter, especially of exercises, has been based on the experience gained in this way.\u003cbr\u003e\u003cbr\u003eR. D. Carmichael.\u003cbr\u003e\u003cbr\u003eContents:\u003cbr\u003e1 ELEMENTARY PROPERTIES OF INTEGERS\u003cbr\u003e 1 Fundamental Notions and Laws \u003cbr\u003e 2 Definition of Divisibility The Unit\u003cbr\u003e 3 Prime Numbers  The Sieve of Eratosthenes\u003cbr\u003e 4 The Number of Primes is Infinite \u003cbr\u003e 5 The Fundamental Theorem of Euclid \u003cbr\u003e 6 Divisibility by a Prime Number \u003cbr\u003e 7 The Unique Factorization Theorem \u003cbr\u003e 8 The Divisors of an Integer \u003cbr\u003e 9 The Greatest Common Factor of Two or More Integers \u003cbr\u003e 10 The Least Common Multiple of Two or More Integers \u003cbr\u003e 11 Scales of Notation \u003cbr\u003e 12 Highest Power of a Prime p Contained in n!\u003cbr\u003e 13 Remarks Concerning Prime Numbers \u003cbr\u003e2 ON THE INDICATOR OF AN INTEGER\u003cbr\u003e 1 Definition\u003cbr\u003e 2 The Indicator of a Product \u003cbr\u003e 3 The Indicator of any Positive Integer \u003cbr\u003e 4 Sum of the Indicators of the Divisors of a Number \u003cbr\u003e3 ELEMENTARY PROPERTIES OF CONGRUENCES\u003cbr\u003e 1 Congruences Modulo m \u003cbr\u003e 2 Solutions of Congruences by Trial \u003cbr\u003e 3 Properties of Congruences Relative to Division \u003cbr\u003e 4 Congruences with a Prime Modulus \u003cbr\u003e 5 Linear Congruences \u003cbr\u003e4 THE THEOREMS OF FERMAT AND WILSON\u003cbr\u003e 1 Fermat's General Theorem \u003cbr\u003e 2 Euler's Proof of the Simple Fermat Theorem \u003cbr\u003e 3 Wilson's Theorem \u003cbr\u003e 4 The Converse of Wilson's Theorem \u003cbr\u003e 5 Impossibility of 1 . 2 . 3... n . 1 + 1 = n^k for n \u0026gt; 5\u003cbr\u003e 6 Extension of Fermat's Theorem \u003cbr\u003e 7 On the Converse of Fermat's Simple Theorem \u003cbr\u003e 8 Application of Previous Results to Linear Congruences \u003cbr\u003e 9 Application of the Preceding Results to the Theory of Quadratic Residues\u003cbr\u003e5 PRIMITIVE ROOTS MODULO m\u003cbr\u003e 1 Exponent of an Integer Modulo m \u003cbr\u003e 2 Another Proof of Fermat's General Theorem \u003cbr\u003e 3 Denition of Primitive Roots \u003cbr\u003e 4 Primitive roots modulo p\u003cbr\u003e 5 Primitive Roots Modulo p, p an Odd Prime \u003cbr\u003e 6 Primitive Roots Modulo 2p, p an Odd Prime \u003cbr\u003e 7 Recapitulation \u003cbr\u003e 8 Primitive  -roots \u003cbr\u003e6 OTHER TOPICS\u003cbr\u003e 1 Introduction \u003cbr\u003e 2 Theory of Quadratic Residues \u003cbr\u003e 3 Galois Imaginaries \u003cbr\u003e 4 Arithmetic Forms \u003cbr\u003e 5 Analytical theory of numbers \u003cbr\u003e 6 Diophantine equations \u003cbr\u003e 7 Pythagorean triangles \u003cbr\u003e 8 The Equation xn + yn = zn","brand":"World Publications CA","offers":[{"title":"Default Title","offer_id":47163734032624,"sku":"2940016797304","price":2.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940016797304_p0.jpg?v=1763642380","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940016797304","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}