On Fixed Points of Iterations Between the Order of Appearance and the Euler Totient Function

Abstract

Let Fn be the nth Fibonacci number. The order of appearance z(n) of a natural number n is defined as the smallest positive integer k such that Fk equivalent to 0(modn). In this paper, we shall find all positive solutions of the Diophantine equation z(phi(n))=n, where phi is the Euler totient function.