# Integer solutions for a vector implicit linear difference equation in ZN

 1Gefter, SL, Goncharuk, AB, Piven', AL1V.N. Karazin Kharkiv National University Dopov. Nac. akad. nauk Ukr. 2018, 11:11-18 https://doi.org/10.15407/dopovidi2018.11.011 Section: Mathematics Language: Ukrainian Abstract:  A criterion of the existence and the uniqueness for an integer solution of the implicit linear difference equation $Ax_{n+1} + Bx_{n} = f_{n}$, where $A$ and $B$ are matrices with integer entries, is proved. Sufficient conditions of the uniqueness for an integer solution of this equation are obtained. Keywords: implicit difference equation, integer solution
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