This paper is concerned with the oscillatory behavior of first order
difference equation with general argument
where
is a sequence of nonnegative real numbers and
is a sequence of integers. Let the number be
defined by . It is proved that, all solutions of Equation () oscillate if the
condition *m>1* is satisfied.

Key Words: Delay difference equation, general argument, oscillation.

2000 Mathematics Subject Classification: Primary: 39A10;

Secondary: 39A21.