A geometric approach to equal sums of fifth powers

Andrew Bremner

Research output: Contribution to journal › Article

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 journal › Article

Bremner, A 1981, 'A geometric approach to equal sums of fifth powers', Journal of Number Theory, vol. 13, no. 3, pp. 337-354. https://doi.org/10.1016/0022-314X(81)90019-6
Bremner A. A geometric approach to equal sums of fifth powers. Journal of Number Theory. 1981;13(3):337-354. https://doi.org/10.1016/0022-314X(81)90019-6
Bremner, Andrew. / A geometric approach to equal sums of fifth powers. In: Journal of Number Theory. 1981 ; Vol. 13, No. 3. pp. 337-354.
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