engleski

On rational Diophantine sextuples

A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuplets. In 1999, Gibbs found the first example of a rational Diophantine sextuple. In this talk, we describe the construction of infinitely many rational Diophantine sextuples. The construction involves elliptic curves, induced by rational Diophantine triples, with torsion group Z/2Z×Z/6Z.

rational Diophantine sextuples ; eliptic curves

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