A property of a class of nonlinear difference equations

Abstract

Abstract.Let g(n) be a rational function of n whose denominator is divisible by the same power of 2 for each n and let au a2, ■ • • be any sequence of rational numbers such that for «>1, On=g(n)(a1an-1+a2a"-2+' ' ' +a"^1a1). In this paper we determine the exact power of 2 dividing the denominator of an for each n and prove congruences (mod 4) and (mod 8).

Properties of the van der Pol numbers and polynomials.

“…Gombining results proved in [5] and [6], we have the following lemma. 2) and the van der Pol numbers enables us to determine the power of 2 dividing V n .…”