A geometric approach to equal sums of fifth powers

Andrew Bremner

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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
Issue number3
StatePublished - Aug 1981
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory


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