Implicit Linear Difference Equation over Residue Class Rings

TL;DR

This paper studies first order implicit linear difference equations over residue class rings modulo m, providing criteria for solution existence, counting solutions, and illustrating the theory with examples.

Contribution

It establishes existence criteria and solution counts for these equations over residue class rings, extending understanding in this mathematical area.

Findings

Derived an existence criterion for solutions.

Established the number of solutions for the equations.

Provided illustrative examples of the theory.

Abstract

We investigate the first order implicit linear difference equation over residue class rings modulo m. We prove an existence criterion and establish the amount of solutions for this equation. We obtain analogous results for the initial problem of the considered equation. The examples which illustrate the developed theory are given.