A geometric approach to equal sums of fifth powers

Andrew Bremner

doi:10.1016/0022-314X(81)90019-6

A geometric approach to equal sums of fifth powers

Andrew Bremner

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

25 Scopus citations

Abstract

Most of the known results about the Diophantine equation x⁵ + y⁵ + z⁵ = u⁵ + v⁵ + w⁵ are shown to be particular instances of a simple geometrical construction. By studying a K3 surface contained in the fourfold, we show that there are an infinity of parametric solutions also satisfying x + y + z = u + v + w, x - y = u - v; and we show that these may be effectively determined.

Original language	English (US)
Pages (from-to)	337-354
Number of pages	18
Journal	Journal of Number Theory
Volume	13
Issue number	3
DOIs	https://doi.org/10.1016/0022-314X(81)90019-6
State	Published - Aug 1981
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/0022-314X(81)90019-6

Cite this

@article{73e37da991904238b10515781ce1a3c2,

title = "A geometric approach to equal sums of fifth powers",

abstract = "Most of the known results about the Diophantine equation x5 + y5 + z5 = u5 + v5 + w5 are shown to be particular instances of a simple geometrical construction. By studying a K3 surface contained in the fourfold, we show that there are an infinity of parametric solutions also satisfying x + y + z = u + v + w, x - y = u - v; and we show that these may be effectively determined.",

author = "Andrew Bremner",

year = "1981",

month = aug,

doi = "10.1016/0022-314X(81)90019-6",

language = "English (US)",

volume = "13",

pages = "337--354",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "3",

}

TY - JOUR

T1 - A geometric approach to equal sums of fifth powers

AU - Bremner, Andrew

PY - 1981/8

Y1 - 1981/8

N2 - Most of the known results about the Diophantine equation x5 + y5 + z5 = u5 + v5 + w5 are shown to be particular instances of a simple geometrical construction. By studying a K3 surface contained in the fourfold, we show that there are an infinity of parametric solutions also satisfying x + y + z = u + v + w, x - y = u - v; and we show that these may be effectively determined.

AB - Most of the known results about the Diophantine equation x5 + y5 + z5 = u5 + v5 + w5 are shown to be particular instances of a simple geometrical construction. By studying a K3 surface contained in the fourfold, we show that there are an infinity of parametric solutions also satisfying x + y + z = u + v + w, x - y = u - v; and we show that these may be effectively determined.

UR - https://www.scopus.com/pages/publications/0000241459

UR - https://www.scopus.com/pages/publications/0000241459#tab=citedBy

U2 - 10.1016/0022-314X(81)90019-6

DO - 10.1016/0022-314X(81)90019-6

M3 - Article

AN - SCOPUS:0000241459

SN - 0022-314X

VL - 13

SP - 337

EP - 354

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 3

ER -

A geometric approach to equal sums of fifth powers

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this