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Dražić, Goran
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 2022/1, Letnik: 116, Številka: 1Journal Article
For a nonzero rational number q , a rational D ( q )- n -tuple is a set of n distinct nonzero rationals { a 1 , a 2 , ⋯ , a n } such that a i a j + q is a square for all 1 ⩽ i < j ⩽ 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 % .
