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

Let F n 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 F k ≡ 0 (mod n) . In this paper, we shall find all positive solutions of the Diophantine equation z (φ (n)) = n , where φ is the Euler totient function. [ABSTRACT FROM AUTHOR]