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- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/08%3A_Topics_in_Number_Theory/8.03%3A_Linear_Diophantine_EquationsVery little is known about Diophantus’ life except that he probably was the first to use letters for unknown quantities in arithmetic problems. His famous work, Arithmetica, consists of approximately ...Very little is known about Diophantus’ life except that he probably was the first to use letters for unknown quantities in arithmetic problems. His famous work, Arithmetica, consists of approximately 130 problems and solutions; most of solutions of equations in various numbers of variables. While Diophantus did not restrict his solutions to the integers and recognized rational number solutions as well, today, however, the solutions for a so-called Diophantine equation must be integers.
- https://math.libretexts.org/Courses/Mount_Royal_University/Higher_Arithmetic/5%3A_Diophantine_Equations/5.1%3A_Linear_Diophantine_EquationsDiophantine equation is a polynomial equation with 2 or more integer unknowns.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Yet_Another_Introductory_Number_Theory_Textbook_-_Cryptology_Emphasis_(Poritz)/02%3A_Congruences/2.02%3A_Linear_CongruencesBecause congruence is analogous to equality, it is natural to ask about the analogues of linear equations, the simplest equations one can solve in algebra, but using congruence rather than equality. I...Because congruence is analogous to equality, it is natural to ask about the analogues of linear equations, the simplest equations one can solve in algebra, but using congruence rather than equality. In this section, we discuss linear congruences of one variable and their solutions.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/An_Introduction_to_the_Theory_of_Numbers_(Moser)/01%3A_Chapters/1.06%3A_Diophantine_EquationsVolume 2 of Dickson’s History of the Theory of Numbers deals with Diophantine equations. It is as large as the other two volumes combined. It is therefore clear that we shall not cover much of this gr...Volume 2 of Dickson’s History of the Theory of Numbers deals with Diophantine equations. It is as large as the other two volumes combined. It is therefore clear that we shall not cover much of this ground in this section. We shall confine our attention to some problems which are interesting though not of central importance.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Raji)/02%3A_Prime_Numbers/2.05%3A_Linear_Diophantine_EquationsIn this section, we discuss equations in two variables called diophantine equations. These kinds of equations require integer solutions. The goal of this section is to present the set of points that d...In this section, we discuss equations in two variables called diophantine equations. These kinds of equations require integer solutions. The goal of this section is to present the set of points that determine the solution to this kind of equations. Geometrically speaking, the diophantine equation represent the equation of a straight line. We need to find the points whose coordinates are integers and through which the straight line passes.
- https://math.libretexts.org/Courses/Mount_Royal_University/Higher_Arithmetic/5%3A_Diophantine_Equations
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/08%3A_Topics_in_Number_Theory/8.03%3A_Linear_Diophantine_EquationsVery little is known about Diophantus’ life except that he probably was the first to use letters for unknown quantities in arithmetic problems. His famous work, Arithmetica, consists of approximately ...Very little is known about Diophantus’ life except that he probably was the first to use letters for unknown quantities in arithmetic problems. His famous work, Arithmetica, consists of approximately 130 problems and solutions; most of solutions of equations in various numbers of variables. While Diophantus did not restrict his solutions to the integers and recognized rational number solutions as well, today, however, the solutions for a so-called Diophantine equation must be integers.
