Pure powers in recurrence sequences and some related diophantine equations. (English) Zbl 0624.10009

Authors’ summary: “We prove that there are only finitely many terms of a nondegenerate linear recurrence sequence which are q-th powers of an integer subject to certain simple conditions on the roots of the associated characteristic polynomial of the recurrence sequence. Further we show by similar arguments that the diophantine equation \(ax^{2t}+bx^ ty+cy^ 2+dx^ t+ey+f=0\) has only finitely many solutions in integers x,y, and t subject to the appropriate restrictions, and we also treat some related simultaneous diophantine equations.”
Reviewer: P.Kiss


11B37 Recurrences
11D04 Linear Diophantine equations
11D41 Higher degree equations; Fermat’s equation
Full Text: DOI


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