When can (((x2 − p)2 − q)2 − r)2 − s2 split into linear factors?

Andrew Bremner

doi:10.1080/10586458.2008.10128879

When can (((x² − p)² − q)² − r)² − s² split into linear factors?

Andrew Bremner

Mathematical and Statistical Sciences, School of (SoMSS)

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

1 Scopus citations

Abstract

We discover two infinite families of integers (P, Q, R, S) such that the polynomial (((X² − P)² − Q)² − R)² − S² factors into linear factors.

Original language	English (US)
Pages (from-to)	385-390
Number of pages	6
Journal	Experimental Mathematics
Volume	17
Issue number	4
DOIs	https://doi.org/10.1080/10586458.2008.10128879
State	Published - 2008

Keywords

Elliptic curve
Nested squares

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1080/10586458.2008.10128879

Cite this

@article{8329387b36ed432bb0daf00d7d6c453d,

title = "When can (((x2 − p)2 − q)2 − r)2 − s2 split into linear factors?",

abstract = "We discover two infinite families of integers (P, Q, R, S) such that the polynomial (((X2 − P)2 − Q)2 − R)2 − S2 factors into linear factors.",

keywords = "Elliptic curve, Nested squares",

author = "Andrew Bremner",

year = "2008",

doi = "10.1080/10586458.2008.10128879",

language = "English (US)",

volume = "17",

pages = "385--390",

journal = "Experimental Mathematics",

issn = "1058-6458",