On a quartic diophantine equation

R.J. Stroeker; B.M.M. Weger, de

doi:10.1017/S0013091500022811

On a quartic diophantine equation

R.J. Stroeker, B.M.M. Weger, de

Research output: Contribution to journal › Article › Academic › peer-review

6 Citations (Scopus)

Abstract

In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and y. We show that this equation does not have any other solutions (x, y) with x¿0 than those given by x = 0,1,2,3,6,91. Two approaches are emphasized, one based on diophantine approximation techniques, the other depends on the structure of certain quartic number fields.

Original language	English
Pages (from-to)	97-114
Journal	Proceedings of the Edinburgh Mathematical Society. Series II
Volume	39
Issue number	1
DOIs	https://doi.org/10.1017/S0013091500022811
Publication status	Published - 1996

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title = "On a quartic diophantine equation",

abstract = "In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and y. We show that this equation does not have any other solutions (x, y) with x¿0 than those given by x = 0,1,2,3,6,91. Two approaches are emphasized, one based on diophantine approximation techniques, the other depends on the structure of certain quartic number fields.",

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AB - In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and y. We show that this equation does not have any other solutions (x, y) with x¿0 than those given by x = 0,1,2,3,6,91. Two approaches are emphasized, one based on diophantine approximation techniques, the other depends on the structure of certain quartic number fields.

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DO - 10.1017/S0013091500022811

M3 - Article

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VL - 39

SP - 97

EP - 114

JO - Proceedings of the Edinburgh Mathematical Society. Series II

JF - Proceedings of the Edinburgh Mathematical Society. Series II

IS - 1

ER -

On a quartic diophantine equation

Abstract

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