In this paper, we study the Diophantine equation $u_n=R(m)P(m)^{Q(m)}$,where $R, P$ and $Q$ are some polynomials (under weak assumptions) and $u_n$ is a Lucas sequence, thus the sequence $(u_n)_{n\geq 0}$ with characteristic ...

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 ...

Let (F-n)(n >= 0) be the sequence of Fibonacci numbers. The order of appearance of an integer n >= 1 is defined as z(n):=min{k >= 1:n vertical bar Fk}. Let Z' be the set of all limit points of {z(n)/n: n >= 1}. By some ...

Let (F-n)(n >= 0) be the Fibonacci sequence. The order of appearance function (in the Fibonacci sequence) z : Z(>= 1)-> Z(>= 1) is defined as z(n) := min{k >= 1 : F-k equivalent to 0 (mod n)}. In this paper, among other ...