Non-Extendable Rational Diophantine 3-Tuples Comprising Polynomialsand Special Figurate Numbers - Sangeetha, Venugopal; Anupreethi, T; Somanath, Manju (Optimality, 2025)
A rational Diophantine 3-tuple is a family of three non-zero rationals x, y, z with the property D(n) such that xy + n, yz + n, xz + n are perfect squares. In this paper, a pair of rational polynomials and some special figurate numbers are scrutinized for their extension as triples and are proved to be non-extendable as quadruples.