We present a method outlined by Euler in his paper{ ``De fractionibus continuis observationes"} {E123} (E123: ``Observations on continued fractions") that can be used to solve homogeneous difference equations with linear coefficients. We will illustrate his ideas by applying it to two familiar examples and explain how it can be understood from a more modern point of view.
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Alexander Aycock (2024) studied this question.
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