PORTUGALIAE MATHEMATICA Vol. 61, No. 1, pp. 124 (2004) 

On the Diophantine equation $G_{n}(x)=G_{m}(P(x))$ for third order linear recurring sequencesClemens FuchsInstitut für Mathematik, Technische Universität Graz,Steyrergasse 30, A8010 Graz  AUSTRIA Email: clemens.fuchs@tugraz.at Abstract: Let ${\bf K}$ be a field of characteristic $0$ and let $a,b,c,G_{0},G_{1},G_{2},P\in{\bf K}[x]$, $\deg P\geq 1$. Further let the sequence of polynomials $(G_{n}(x))_{n=0}^{\infty}$ be defined by the third order linear recurring sequence Keywords: Diophantine equations; ternary linear recurring sequences; $S$unit equations. Classification (MSC2000): 11D45, 11D04, 11D61, 11B37. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2004 Sociedade Portuguesa de Matemática
