Diophantine quintuples containing triples of the first kind

David J Platt, Timothy Trudgian

Research output: Contribution to journalArticle (Academic Journal)peer-review

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We consider Diophantine quintuples {a, b, c, d, e}, sets of integers with a < b < c < d < e the product of any two elements of which is one less than a perfect square. Triples of the first kind are sets {A, B,C} with C ≥ B5. We show that there are no Diophantine quintuples {a, b, c, d, e} such that {a, b, d} is a triple of the first kind.
Original languageEnglish
Pages (from-to)235-242
Number of pages8
JournalPeriodica Mathematica Hungarica
Issue number2
Early online date18 Apr 2016
Publication statusPublished - 1 Jun 2016


  • Diophantine quintuples
  • Simultaneous solution to Pell equations


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