In this paper we consider a particular class of polynomials arising from the solutions of the Diophantine equation (x+y−1)2 = wxy. We highlight some interesting aspects, describing their relationship with many iportant integer sequences and pointing out their connection with Dickson and Chebyshev polynomials. We also study their coefficients finding a new identity involving Catalan numbers and proving that they are a Riordan array.
On polynomial solutions of the Diophantine equation (x+y-1)^2 = wxy / Barbero, Stefano; Cerruti, Umberto; Murru, Nadir. - In: RENDICONTI DEL SEMINARIO MATEMATICO. - ISSN 0373-1243. - 2020/78:1(2020), pp. 5-12.
On polynomial solutions of the Diophantine equation (x+y-1)^2 = wxy
Murru, Nadir
2020-01-01
Abstract
In this paper we consider a particular class of polynomials arising from the solutions of the Diophantine equation (x+y−1)2 = wxy. We highlight some interesting aspects, describing their relationship with many iportant integer sequences and pointing out their connection with Dickson and Chebyshev polynomials. We also study their coefficients finding a new identity involving Catalan numbers and proving that they are a Riordan array.| File | Dimensione | Formato | |
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