Note on a discrete initial value problem from a competition

Abstract

The following discrete initial value problem xn+1=xn(xn−12−2)−x1,n∈N,x= 2 and x1= 5 / 2 , appeared at an international competition. It is known that the problem can be solved in closed form. Here we discuss the solvability of a more general initial value problem which includes the former one. We show that, in a sense, there are not so many solvable discrete initial value problems related to this one, showing its specificity, which is a bit surprising result.