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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


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
MathSciNet review: 1308461
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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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PII: S 0025-5718(1995)1308461-7
Keywords: Hilbert's Tenth Problem, Diophantine equations, quadratic forms, factoring integers
Article copyright: © Copyright 1995 American Mathematical Society