 
Summary: Rational solutions of linear di#erence and qdi#erence
equations with polynomial coe#cients #
S.A.Abramov
Computer Center of the Russian Academy of Science
Vavilova 40, Moscow 117967, Russia
abramov@ccas.ru
Abstract
We propose a simple algorithm to construct a polynomial divisible by the denomi
nator of any rational solution of a linear di#erence equation
a n (x)y(x + n) + . . . + a 0 (x)y(x) = b(x)
with polynomial coe#cients and a polynomial righthand side. Then we solve the same
problem for qdi#erence equations.
Nonhomogeneous equations with hypergeometric righthand sides are considered as
well.
§1.Di#erence equations
Consider the problem of finding all rational solutions of linear di#erence equations of the
form
a n (x)y(x + n) + . . . + a 0 (x)y(x) = b(x) (1)
or in operator form, Ly(x) = b(x), where
L = a n (x)E n + . . . + a 1 (x)E + a 0 (x). (2)
