Integer solutions for a vector implicit linear difference equation in ZN

1Gefter, SL, Goncharuk, AB, Piven', AL
1V.N. Karazin Kharkiv National University
Dopov. Nac. akad. nauk Ukr. 2018, 11:11-18
Section: Mathematics
Language: Ukrainian
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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