Abstract
We prove that, for every k ∈ ℕ, the following generalization of the Putnam difference equation
has a positive solution with the following asymptotics
for some c > 1 depending on k, and where λ is the root of the polynomial P(λ) = λ k+2 − λ − 1 belonging to the interval (1, 2). Using this result, we prove that the equation has a positive solution which is not eventually equal to 1. Also, for the case k = 1, we find all positive eventually equal to unity solutions to the equation.
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Published in Russian in Matematicheskie Zametki, 2008, Vol. 84, No. 5, pp. 772–780.
The text was submitted by the author in English.
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Stević, S. Nontrivial solutions of a higher-order rational difference equation. Math Notes 84, 718–724 (2008). https://doi.org/10.1134/S0001434608110138
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DOI: https://doi.org/10.1134/S0001434608110138