Studies on the difference equationx_n+1 = 1/(x_n+x_n − 2)

Abstract

Using direct and elementary methods, we prove that the solution of under the initial conditions is asymptotically two-periodic prime. It answers the Conjecture stated by Camouzis and Ladas. In addition, we study some generalizations of the conjecture applied to other equations, give a numerical and graphical description of the basin of attraction of the positive equilibrium point and analyse numerically the bad set of this equation.