A new proof of a conjecture of Antoniadis

Zhenfu Cao; Shanzhi Mu; Xiaolei Dong

doi:10.1006/jnth.1999.2489

A new proof of a conjecture of Antoniadis

Zhenfu Cao^*, Shanzhi Mu, Xiaolei Dong

^*Corresponding author for this work

Harbin Institute of Technology

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

3 Scopus citations

Abstract

We give a new and elementary proof that the equation x³-1=31y² has only the integral solutions (x, y)=(1, 0), (5, 2), (5, -2).

Original language	English
Pages (from-to)	185-193
Number of pages	9
Journal	Journal of Number Theory
Volume	83
Issue number	2
DOIs	https://doi.org/10.1006/jnth.1999.2489
State	Published - Aug 2000
Externally published	Yes

Keywords

Cubic diophantine equation
Legendre-Jacobi symbol
Recurrence sequence

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10.1006/jnth.1999.2489

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@article{a4dede98b7a041f2b10aff8a0a6f35b6,

title = "A new proof of a conjecture of Antoniadis",

abstract = "We give a new and elementary proof that the equation x3-1=31y2 has only the integral solutions (x, y)=(1, 0), (5, 2), (5, -2).",

keywords = "Cubic diophantine equation, Legendre-Jacobi symbol, Recurrence sequence",

author = "Zhenfu Cao and Shanzhi Mu and Xiaolei Dong",

year = "2000",

month = aug,

doi = "10.1006/jnth.1999.2489",

language = "英语",

volume = "83",

pages = "185--193",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "2",

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T1 - A new proof of a conjecture of Antoniadis

AU - Cao, Zhenfu

AU - Mu, Shanzhi

AU - Dong, Xiaolei

PY - 2000/8

Y1 - 2000/8

N2 - We give a new and elementary proof that the equation x3-1=31y2 has only the integral solutions (x, y)=(1, 0), (5, 2), (5, -2).

AB - We give a new and elementary proof that the equation x3-1=31y2 has only the integral solutions (x, y)=(1, 0), (5, 2), (5, -2).

KW - Cubic diophantine equation

KW - Legendre-Jacobi symbol

KW - Recurrence sequence

UR - https://www.scopus.com/pages/publications/0034238995

U2 - 10.1006/jnth.1999.2489

DO - 10.1006/jnth.1999.2489

M3 - 文章

AN - SCOPUS:0034238995

SN - 0022-314X

VL - 83

SP - 185

EP - 193

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 2

ER -

A new proof of a conjecture of Antoniadis

Abstract

Keywords

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