engleski

Rational D(q)-quintuples

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%.

Diophantine m-tuples, D(q)-m-tuples, Elliptic Curves, Twists, Rank, Parity Conjecture

nije evidentirano