Diophantine equations for second-order recursive sequences of polynomials

Authors
Dujella, A Tichy, RF
Citation
A. Dujella et Rf. Tichy, Diophantine equations for second-order recursive sequences of polynomials, Q J MATH, 52, 2001, pp. 161-169
Citations number
13
Categorie Soggetti
Mathematics
Journal title
QUARTERLY JOURNAL OF MATHEMATICS
ISSN journal
00335606 → ACNP
Volume
52
Year of publication
2001
Part
2
Pages
161 - 169
Database
ISI
SICI code
0033-5606(200106)52:<161:DEFSRS>2.0.ZU;2-#
Abstract
Let B be a non-zero integer. Define the sequence of polynomials G(n)(x) by G(0)(x) = 0, G(1)(x) = 1, G(n+1)(x) = (x)G(n)(x) + BG(n-1)(x), n epsilon N. We prove that the diophantine equation G(m)(x) = G(n)(y) for m, n greater than or equal to 3, m not equal n, has only finitely many solutions.