An implicit linear difference equation over the ring of integers is considered as an infinite system of linear equations with integer coefficients. Under certain assumptions on coefficients, we show that the system has a unique solution in integers and this solution can be found by an analogue of the Cramer rule. The main constructions are based on the use of the p-adic topology of the ring of integers.
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Translated from Problemy Matematicheskogo Analiza101, 2019, pp. 57-62.
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Gefter, S.L., Martseniuk, V.V., Goncharuk, A.B. et al. Analogue of the Cramer Rule for an Implicit Linear Second Order Difference Equation Over the Ring of Integers. J Math Sci 244, 601–607 (2020). https://doi.org/10.1007/s10958-019-04635-w
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DOI: https://doi.org/10.1007/s10958-019-04635-w