Diophantine equations for Morgan-Voyce and other modified orthogonal polynomials View Full Text


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Article Info

DATE

2008-02

AUTHORS

Thomas Stoll, Robert F. Tichy

ABSTRACT

It is well-known that Morgan-Voyce polynomials Bn(x) and bn(x) satisfy both a Sturm-Liouville equation of second order and a three-term recurrence equation ([SWAMY, M.: Further properties of Morgan-Voyce polynomials, Fibonacci Quart. 6 (1968), 167–175]). We study Diophantine equations involving these polynomials as well as other modified classical orthogonal polynomials with this property. Let A, B, C ∈ ℚ and {pk(x)} be a sequence of polynomials defined by with with A ≠ 0, B > 0 in the first, B ≠ 0 in the second and C > −¼B2 in the third case. We show that the Diophantine equation with m > n ≥ 4, ≠ 0 has at most finitely many solutions in rational integers x, y. More... »

PAGES

11-18

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.2478/s12175-007-0051-2

DOI

http://dx.doi.org/10.2478/s12175-007-0051-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1019806300


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