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

23 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

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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",

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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.

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A geometric approach to equal sums of fifth powers

Abstract

ASJC Scopus subject areas

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