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The Quarterly Journal of Mathematics 2001 52(2):161-169; doi:10.1093/qjmath/52.2.161
© 2001 by Oxford University Press
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Diophantine Equations for Second-Order Recursive Sequences of Polynomials

Andrej Dujella1 and Robert F. Tichy2

1 Department of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb, Croatia. E-mail: duje@math.hr 2 Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria. E-mail: tichy@weyl.math.tu-graz.ac.at

Let B be a non-zero integer. Define the sequence of polynomials nG(x) by G0(x) = 0, G1(x) = 1, Gn+1(x) = nxG(x) + BGn–1(x), n N. We prove that the diophantine equation mG(x) = nG(y) for m, n ≥ 3, m != n, has only finitely many solutions.


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