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 identities.

Polynomial sequences on quadratic curves

CERRUTI, Umberto;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 identities.
15
Articolo A38
1
14
http://arxiv.org/abs/1512.03182v1
Mathematics - Number Theory;
Marco, Abrate; Stefano, Barbero; Umberto, Cerruti; Nadir, Murru
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1605657
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