Glasnik Matematicki, Vol. 41, No.2 (2006), 195-203.

SOME RATIONAL DIOPHANTINE SEXTUPLES

Philip Gibbs

Abstract.   A famous problem posed by Diophantus was to find sets of distinct positive rational numbers such that the product of any two is one less than a rational square. Some sets of six such numbers are presented and the computational algorithm used to find them is described. A classification of quadruples and quintuples with examples and statistics is also given.

2000 Mathematics Subject Classification.   11D09.

Key words and phrases.   Diophantine sextuple, regular Diophantine quintuple, irregular Diophantine quintuple.

DOI: 10.3336/gm.41.2.02

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