A geometric approach to equal sums of fifth powers

Research output: Contribution to journalArticle

22 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)337-354
Number of pages18
JournalJournal of Number Theory
Volume13
Issue number3
DOIs
StatePublished - 1981
Externally publishedYes

Fingerprint

Parametric Solutions
K3 Surfaces
Diophantine equation
Geometric Approach
Infinity

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

A geometric approach to equal sums of fifth powers. / Bremner, Andrew.

In: Journal of Number Theory, Vol. 13, No. 3, 1981, p. 337-354.

Research output: Contribution to journalArticle

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