Summary: In this paper we introduce and investigate the so-called quasi-Fibonacci numbers of order 11 . These numbers are defined by five conjugate recurrence equations of order five. We study some relations and identities concerning these numbers. We present some applications to the decomposition of some polynomials. Many of the identities presented here are the generalizations of the identities characteristic for general recurrence sequences of order three given by Rabinowitz.

Fibonacci numbers, primitive roots of unity, recurrence relation