{"product_id":"diophantine-equations-and-systems-an-introduction-a-systematic-approach-to-problem-solving-paperback","title":"Diophantine Equations and Systems: An Introduction: A systematic approach to problem solving - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eDemetrios P. Kanoussis Ph. D.\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eDiophantine equations are polynomial equations with integer coefficients for which only integer solutions are sought. In his great work \"\u003cb\u003eArithmetica\u003c\/b\u003e\", the Greek mathematician \u003cb\u003eDiophantus of Alexandria, \u003c\/b\u003e (born in Alexandria Egypt in 200 AD and died in 284 AD), known as the father of Algebra, studied and solved such types of equations, (integer coefficients and integer solutions), of the first up to the fourth degree. These equations are now known as \"\u003cb\u003eDiophantine equations\u003c\/b\u003e\". A characteristic feature of Diophantine equations is that in these equations the number of equations is smaller than the number of unknowns. For example, we may have one equation with two unknowns, or one equation with three unknowns, or a system of two equations with three unknowns, etc. While in the set of real numbers R these types of equations, (fewer equations than number of unknowns), are indeterminate, in the set of integers Z={... -3, -2, -1,0,1,2,3, ...} or in the set of natural numbers N={1,2,3,4, ...}, these equations may or may not have integer solutions, (depending on the coefficients of the equations).\u003cbr\u003eIn this book we provide a systematic introduction to Diophantine equations, with emphasis on the solution of various problems. The first two chapters are devoted to first degree Diophantine equations and systems, (linear equations and systems), while the third chapter is devoted to second degree Diophantine equations and systems. Among other equations, in this chapter, we study the \u003cb\u003ePythagorean equation\u003c\/b\u003e (x 2+y 2=z 2), and the \u003cb\u003ePell's equation\u003c\/b\u003e (x 2-ky 2=1). The solution of Pell's equation is achieved by a really brilliant method, which is attributed to \u003cb\u003eLagrange\u003c\/b\u003e. Various examples of higher degree Diophantine equations are considered in chapter 4. The analytic description of the material covered in this book can be found in the table of contents.\u003cbr\u003eThe book is concluded with a collection of 40 miscellaneous, challenging problems, with answers and detailed remarks and hints.\u003cbr\u003eIn total, the book contains 55 solved examples and 105 problems for solution.\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 96\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.2 x 10 x 7 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e March 08, 2024\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47510197403897,"sku":"9798884186637","price":16.07,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/oex-j6SA7l9798884186637.webp?v=1773385011","url":"https:\/\/bookscloud.io\/products\/diophantine-equations-and-systems-an-introduction-a-systematic-approach-to-problem-solving-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}