Abstract
For nonnegative real numbers 
, 
, 
, 
, 
, 
and 
such that 
and 
, the difference equation 
, 
has a unique positive equilibrium. A proof is given here for the following statements: (1) For every choice of positive parameters
, 
, 
, 
, 
, 
and 
, all solutions to the difference equation
, 
converge to the positive equilibrium or to a prime period-two solution. (2) For every choice of positive parameters
, 
, 
, 
, 
and 
, all solutions to the difference equation
, 
converge to the positive equilibrium or to a prime period-two solution.