Eventually constant solutions of a rational difference equation |
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| Authors: | Bratislav Iri
anin Stevo Stevi&#x; |
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| Institution: | aFaculty of Electrical Engineering, Bulevar Kralja Aleksandra 73, 11000 Beograd, Serbia;bMathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia |
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| Abstract: | We describe all the solutions of a rational difference equation from Putnam’s mathematical competition, which are eventually equal to its positive equilibrium  . As a consequence we give a new, elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one. Moreover, we show that almost all solutions of the equation are not eventually equal to one. |
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| Keywords: | Rational difference equation Positive solutions Eventually equal to unity |
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