Solutions of the Difference Equation xn+1=xnxn−1−1

الملخص EN

Our goal in this paper is to investigate the long-term behavior of solutions of the following difference equation: xn+1=xnxn−1−1, n=0,1,2,…, where the initial conditions x−1 and x0 are real numbers.

We examine the boundedness of solutions, periodicity of solutions, and existence of unbounded solutions and how these behaviors depend on initial conditions.