Little Mathematics Library 
Solving Equations In Integers by I. M.  Gelfond also sometimes written as
 Gelfand. 

Israel Gelfand is an highly accomplished mathematician who is also a
 pedagogue, and has written several texts at elementary level apart
 from numerous higher level texts. They include  Algebra,
 Trigonometry, Functions and Graphs, Combinatorics, Method of
 Coordinates. 

The book is devoted to one of the most interesting branches of
number theory, the solution of equations in integers. The solution
in integers of algebraic equations in more than one unknown with
integral coefficients is a most difficult problem in the theory of
numbers. The theoretical importance of equations with integral
coefficients is quite great as they are closely connected with many
problems of number theory. Moreover, these equations are
sometimes encountered in physics and so they are also
important in practice. The elements of the theory of equations with
integral coefficients as presented in this book are suitable for
broadening the mathematical outlook of high-school students and
students of pedagogical institutes. Some of the main results in the
theory of the solution of equations in integers have been given and
proofs of the theorems involved are supplied when they are
sufficiently simple.


 The book was translated the Russian by O. B. Sheinin and was first published by Mir in 1981.

  PDF | Cover | Bookmarks | OCR | 3.2 MB | 60 pp | 600 dpi

  
  Released on TPB by mirtitles.org


Contents
Preface 7
Introduction 7
1. Equations in one unknown. 8
2. Linear equations in two unknowns 9
3. Equations of the second degree in three unknowns (examples) 18
4. Equations of the type x^2 - Ay^2 = 1. Finding an solutions of this equation 23
5. Equations of the second degree in two unknowns: the general case 33
6. Equations in two unknowns of degree higher than the second 44
7. Algebraic equations in three unknowns of degree higher than
the second. Some exponential equations 49