On Diophantine triples and quadruples

George Grossman, Yifan Zhang

Research output: Contribution to journalArticlepeer-review


In this paper we consider Diophantine triples fa; b; cg; (denoted D(n)-3-tuples) and give necessary and sufficient conditions for existence of integer n given the 3-tuple fa; b; cg; so that ab + n; ac + n; bc + n are all squares of integers. Several examples as applications of the main results, related to both Diophantine triples and quadruples, are given.
Original languageEnglish
Pages (from-to)5-16
JournalNotes on Number Theory and Discrete Mathematics
Issue number4
StatePublished - 2015


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