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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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An algorithm for solving a certain class of Diophantine equations. I
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by David Lee Hilliker PDF
Math. Comp. 38 (1982), 611-626 Request permission

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.
References
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 38 (1982), 611-626
  • MSC: Primary 10B15; Secondary 10-04
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0645676-6
  • MathSciNet review: 645676