The Diophantine Equation x4 + 1 = Dy2

An effective method is derived for solving the equation of the title in positive integers x and y for given D completely, and is carried out for all $D < 100000$. If D is of the form m4 + 1, then there is the solution x = m, y = 1; in the above range, except for D = 70258 with solution x = 261, y...

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Veröffentlicht in:	Mathematics of computation 1997-07, Vol.66 (219), p.1347-1351
1. Verfasser:	Cohn, J. H. E.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Diophantine equation Exact sciences and technology Factorization Integers Mathematical induction Mathematics Number theory Sciences and techniques of general use
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	An effective method is derived for solving the equation of the title in positive integers x and y for given D completely, and is carried out for all $D < 100000$. If D is of the form m4 + 1, then there is the solution x = m, y = 1; in the above range, except for D = 70258 with solution x = 261, y = 257, there are no other solutions.
ISSN:	0025-5718 1088-6842