Two more representation problems

Andrew Bremner, Richard K. Guy

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We discuss the problem of finding those integers which may be represented by (x + y + z)3/xyz, and also those which may be represented by x/y + y/z + z/x, where x, y, z are integers. For example, x = -3888953655693309094309277243253295616000, y = 870614350109377939730940722158565152629, z = -211788680591112853611774198484237121509 satisfy (x + y + z)3/(xyz) = -47, and x = 10695607136243980529530429582617991136107507407713992824, y = -123256655541019041417443728014061733054947136623569984, z = 8446121230200308492574953446465639841507828834632079329 satisfy x/y + y/z + z/x = -86.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalProceedings of the Edinburgh Mathematical Society
Volume40
Issue number1
StatePublished - 1997

Fingerprint

Integer

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Two more representation problems. / Bremner, Andrew; Guy, Richard K.

In: Proceedings of the Edinburgh Mathematical Society, Vol. 40, No. 1, 1997, p. 1-17.

Research output: Contribution to journalArticle

@article{47fd2145aefd4defbb0479f5727b9520,
title = "Two more representation problems",
abstract = "We discuss the problem of finding those integers which may be represented by (x + y + z)3/xyz, and also those which may be represented by x/y + y/z + z/x, where x, y, z are integers. For example, x = -3888953655693309094309277243253295616000, y = 870614350109377939730940722158565152629, z = -211788680591112853611774198484237121509 satisfy (x + y + z)3/(xyz) = -47, and x = 10695607136243980529530429582617991136107507407713992824, y = -123256655541019041417443728014061733054947136623569984, z = 8446121230200308492574953446465639841507828834632079329 satisfy x/y + y/z + z/x = -86.",
author = "Andrew Bremner and Guy, {Richard K.}",
year = "1997",
language = "English (US)",
volume = "40",
pages = "1--17",
journal = "Proceedings of the Edinburgh Mathematical Society",
issn = "0013-0915",
publisher = "Cambridge University Press",
number = "1",

}

TY - JOUR

T1 - Two more representation problems

AU - Bremner, Andrew

AU - Guy, Richard K.

PY - 1997

Y1 - 1997

N2 - We discuss the problem of finding those integers which may be represented by (x + y + z)3/xyz, and also those which may be represented by x/y + y/z + z/x, where x, y, z are integers. For example, x = -3888953655693309094309277243253295616000, y = 870614350109377939730940722158565152629, z = -211788680591112853611774198484237121509 satisfy (x + y + z)3/(xyz) = -47, and x = 10695607136243980529530429582617991136107507407713992824, y = -123256655541019041417443728014061733054947136623569984, z = 8446121230200308492574953446465639841507828834632079329 satisfy x/y + y/z + z/x = -86.

AB - We discuss the problem of finding those integers which may be represented by (x + y + z)3/xyz, and also those which may be represented by x/y + y/z + z/x, where x, y, z are integers. For example, x = -3888953655693309094309277243253295616000, y = 870614350109377939730940722158565152629, z = -211788680591112853611774198484237121509 satisfy (x + y + z)3/(xyz) = -47, and x = 10695607136243980529530429582617991136107507407713992824, y = -123256655541019041417443728014061733054947136623569984, z = 8446121230200308492574953446465639841507828834632079329 satisfy x/y + y/z + z/x = -86.

UR - http://www.scopus.com/inward/record.url?scp=33747394312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747394312&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33747394312

VL - 40

SP - 1

EP - 17

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 1

ER -