Rational D(q)-quintuples

2021/05/13 by Dražić, Goran · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2105.06574

Abstract

For a nonzero rational number q, a rational D(q)-n-tuple is a set of n distinct nonzero rationals \a₁, a₂, …, a_n\ such that a_ia_j+q is a square for all 1 \leqslant i < j \leqslant n. We investigate for which q there exist infinitely many rational D(q)-quintuples. We show that assuming the Parity Conjecture for the twists of several explicitly given elliptic curves, the density of such q is at least 295026/296010≈ 99.5%.

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