The global attractivity of the rational difference equation $y_{n}=1+\frac{y_{n-k}}{y_{n-m}}$

Kenneth S. Berenhaut, John D. Foley, Stevo Stević
2007 Proceedings of the American Mathematical Society  
This paper studies the behavior of positive solutions of the recursive equation with y −s , y −s+1 , . . . , y −1 ∈ (0, ∞) and k, m ∈ {1, 2, 3, 4, . . .}, where s = max{k, 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.
doi:10.1090/s0002-9939-06-08580-7 fatcat:fs5jxfvgjzb45bkeyc2czed6oi