MATHEMATICS Proceedings A 89 (l), March 24, 1986 Distribution of the ratios of the terms of a second order linear recurrence by PBter Kiss’ and Robert F. Tichy2 ’ Teacher’s Training College, 3300 Eger, Hungary ’ Abteilung fiir Technische Mathematik, TU- Wien. Wiedner Hauptstrasse 6-10, A-1040 Wien, Austria Communicated by Prof. J.H. van Lint at the meeting of October 28, 1985 1. INTRODUCTION Let G = (G,),“=, be a second order linear recurring sequence defined by (1) G,=A-G,-,+B.G,-, (nz2), with non-zero real coefficients A, B and real initial values Go, Gi supposing that Gi #O. The discriminant D=A2+4B of the characteristic polynomial f(x) =x*-Ax-B of the recursion (1) is said to be the discriminant of G. It is well-known that the terms of G can be ex- pressed as (2) G, = aa” + bp”, if the characteristic polynomial has two distinct roots a, p and (3) G - PGo G, - crGo a= a-8 , b= P-a . The object of this paper is the investigation of the distribution behaviour of the set ((Gi/Gj}), where G is a second order linear recurrence of real numbers with negative discriminant D; {t} denotes the fractional part of the real number t. We determine the asymptotic distribution function of the sequence ((G,, ,/Gn}),“=, and give an estimate of the error term. 79