A rational Diophantine $m$-tuple is a set of $m$ nonzero rationals such that the product of any two of them is one less than a perfect square. Recently Gibbs constructed several examples of rational Diophantine sextuples with positive elements. In this note, we construct examples of rational Diophantine sextuples with mixed signs. Indeed, we show that such examples exist for all possible combinations of signs.
"Rational Diophantine sextuples with mixed signs." Proc. Japan Acad. Ser. A Math. Sci. 85 (4) 27 - 30, April 2009. https://doi.org/10.3792/pjaa.85.27