In this paper we generalize the study of Matiyasevich on integer points over conics, introducing the more general concept of radical points. With this generalization we are able to solve in positive integers some Diophantine equations, relating these solutions by means of particular linear recurrence sequences. We point out interesting relationships between these sequences and known sequences in OEIS. We finally show connections between these sequences and Chebyshev and Morgan-Voyce polynomials, finding new dentities
Polynomial sequences on quadratic curves / Abrate, Marco; Barbero, Stefano; Cerruti, Umberto; Murru, Nadir. - In: INTEGERS. - ISSN 1553-1732. - 15:38(2015), pp. 1-14.
Polynomial sequences on quadratic curves
Barbero, Stefano;Murru, Nadir
2015-01-01
Abstract
In this paper we generalize the study of Matiyasevich on integer points over conics, introducing the more general concept of radical points. With this generalization we are able to solve in positive integers some Diophantine equations, relating these solutions by means of particular linear recurrence sequences. We point out interesting relationships between these sequences and known sequences in OEIS. We finally show connections between these sequences and Chebyshev and Morgan-Voyce polynomials, finding new dentities| File | Dimensione | Formato | |
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