The global attractivity of the rational difference equation yn =1

This paper studies the behavior of positive solutions of the recur-sive equation y n = 1 + y n−k y n−m We prove that if gcd(k, m) = 1, with k odd, then y n tends to 2, exponentially. When combined with a recent result of E., this answers the question when y = 2 is a global attractor.