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

Access to Document

10.1017/S0013091500022811

Cite this

@article{c18f11fb6720440f9c813155d27c4942,

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.",

author = "R.J. Stroeker and {Weger, de}, B.M.M.",

year = "1996",

doi = "10.1017/S0013091500022811",

language = "English",

volume = "39",

pages = "97--114",

journal = "Proceedings of the Edinburgh Mathematical Society. Series II",

issn = "0013-0915",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - On a quartic diophantine equation

AU - Stroeker, R.J.

AU - Weger, de, B.M.M.

PY - 1996

Y1 - 1996

N2 - 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.

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.

U2 - 10.1017/S0013091500022811

DO - 10.1017/S0013091500022811

M3 - Article

VL - 39

SP - 97

EP - 114

JO - Proceedings of the Edinburgh Mathematical Society. Series II

JF - Proceedings of the Edinburgh Mathematical Society. Series II

SN - 0013-0915

IS - 1

ER -

On a quartic diophantine equation

Abstract

Access to Document

Fingerprint

Cite this