48 more solutions of Martin Davis's quaternary quartic equation

Authors:
Daniel Shanks and Samuel S. Wagstaff

Journal:
Math. Comp. **64** (1995), 1717-1731

MSC:
Primary 11D25; Secondary 11Y50

DOI:
https://doi.org/10.1090/S0025-5718-1995-1308461-7

MathSciNet review:
1308461

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Abstract | References | Similar Articles | Additional Information

Abstract: We find 48 more solutions to a Diophantine equation investigated by Martin Davis. Before our work, only two solutions were known. Construction of the new solutions required the factorization of several large integers. Because the equation relates to Hilbert's Tenth Problem it is desirable to know if it has only finitely many solutions. An elaborate argument is given for the conjecture that the equation has infinitely many solutions in integers.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1995-1308461-7

Keywords:
Hilbert's Tenth Problem,
Diophantine equations,
quadratic forms,
factoring integers

Article copyright:
© Copyright 1995
American Mathematical Society