Equal sums of two cubes of quadratic forms

Research output: Contribution to journalArticlepeer-review


We give a complete description of all solutions to the equation f13 + f 23 = f 33 + f 43 for quadratic forms fj [x,y] and show how Ramanujan's example can be extended to three equal sums of pairs of cubes. We also give a complete census in counting the number of ways a sextic p [x,y] can be written as a sum of two cubes. The extreme example is p(x,y) = xy(x4 - y4), which has six such representations.

Original languageEnglish (US)
Pages (from-to)761-786
Number of pages26
JournalInternational Journal of Number Theory
Issue number3
StatePublished - Apr 2021


  • Cubic forms
  • diophantine equations
  • sextic forms

ASJC Scopus subject areas

  • Algebra and Number Theory


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