Abstract
In this research work, some cases on the periodicity of the difference equation
y(n+1) = p(0)y(n) + p(1)y(n-f) + p(2)y(n-m) + p(3)y(n-k) + p(4)y(n-s)/q(0)y(n) + q(1)y(n-f) + q(2)y(n-m) + q(3)y(n-k) + q(4)y(n-s), n=0,1,2,...,
arc investigated, where the coefficients p(t), q(i) is an element of(0,infinity), i = 0, ..., 4 and f, m, k and s are positive integers. The initial conditions y(-s), ..., y(-k), ..., y(-m), ..., y(-f), ..., y(-1), y(0) are arbitrary positive real numbers such that f < m < k < s. Some numerical examples will be given to illustrate our result.