An algorithm for solving a certain class of Diophantine equations. I-Reference-Cited by-同舟云学术

An algorithm for solving a certain class of Diophantine equations. I

Published:1982 Issue:158 Volume:38 Page:611-626
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Hilliker David Lee

Abstract

A class of Diophantine equations is defined and an algorithm for solving each equation in this class is developed. The methods consist of techniques for the computation of an upper bound for the absolute value of each solution. The computability of these bounds is guaranteed. Typically, these bounds are well within the range of computer programming and so they constitute a practical method for computing all solutions to the Diophantine equation in question. As a first application, a bound for a cubic equation is computed. As a second application, a set of quartic equations is studied. Methods are developed for deriving various sets of conditions on the coefficients in such equations under which a bound exists and can be computed.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1982-38-158/S0025-5718-1982-0645676-6/S0025-5718-1982-0645676-6.pdf

Reference17 articles.

1. Transcendental Number Theory

2. On the solvability of the Diophantine equation 𝑎𝑥²+𝑏𝑦²+𝑐𝑧²=0 in imaginary Euclidean quadratic fields;Hemer, Ove;Ark. Mat.,1952

3. David Lee Hilliker, "An algorithm for solving a certain class of Diophantine equations. II," (to be submitted).

4. David Lee Hilliker & Ray Steiner, "On Mordell’s Diophantine equation," (to be submitted).

5. David Lee Hilliker & E. G. Straus, "On Puiseux series whose curves pass through an infinity of algebraic lattice points," (to be submitted).