A note on a parameterized family of quartic thue equations

Shexi Chen; Zhigang Li

doi:10.17654/MS101051095

A note on a parameterized family of quartic thue equations

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

Abstract

In this paper, by the method of Tzanakis, we give all integral solutions of parameterized quartic Thue equation x⁴ − 4sx³ y + (12s − 4)x² y² − 8sxy³ + 4y⁴ = 1, s > 18, which are (x, y) = (1, 1), (−1, −1), (1, 0), (−1, 0).

Original language	English
Pages (from-to)	1095-1104
Number of pages	10
Journal	Far East Journal of Mathematical Sciences
Volume	101
Issue number	5
DOIs	https://doi.org/10.17654/MS101051095
Publication status	Published - Mar 2017
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2017 Pushpa Publishing House, Allahabad, India.

Keywords

Davenport lemma
Equation
Tzanakis method

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10.17654/MS101051095

Cite this

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title = "A note on a parameterized family of quartic thue equations",

abstract = "In this paper, by the method of Tzanakis, we give all integral solutions of parameterized quartic Thue equation x4 − 4sx3 y + (12s − 4)x2 y2 − 8sxy3 + 4y4 = 1, s > 18, which are (x, y) = (1, 1), (−1, −1), (1, 0), (−1, 0).",

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author = "Shexi Chen and Zhigang Li",

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year = "2017",

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language = "English",

volume = "101",

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AU - Chen, Shexi

AU - Li, Zhigang

PY - 2017/3

Y1 - 2017/3

N2 - In this paper, by the method of Tzanakis, we give all integral solutions of parameterized quartic Thue equation x4 − 4sx3 y + (12s − 4)x2 y2 − 8sxy3 + 4y4 = 1, s > 18, which are (x, y) = (1, 1), (−1, −1), (1, 0), (−1, 0).

AB - In this paper, by the method of Tzanakis, we give all integral solutions of parameterized quartic Thue equation x4 − 4sx3 y + (12s − 4)x2 y2 − 8sxy3 + 4y4 = 1, s > 18, which are (x, y) = (1, 1), (−1, −1), (1, 0), (−1, 0).

KW - Davenport lemma

KW - Equation

KW - Tzanakis method

UR - https://www.scopus.com/pages/publications/85013916903

U2 - 10.17654/MS101051095

DO - 10.17654/MS101051095

M3 - Journal Article

AN - SCOPUS:85013916903

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VL - 101

SP - 1095

EP - 1104

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

IS - 5

ER -

A note on a parameterized family of quartic thue equations

Abstract

Bibliographical note

Keywords

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