On Fibonacci Numbers of Order r Which Are Expressible as Sum of Consecutive Factorial Numbers

On perfect numbers which are ratios of two Fibonacci numbers ∗

Here, we prove that there is no perfect number of the form Fmn/Fm, where Fk is the kth Fibonacci number.

On Fibonacci numbers which are elliptic Korselt numbers

Here, we show that if E is a CM elliptic curve with CM field Q( √ −d), then the set of n for which the nth Fibonacci number Fn satisfies an elliptic Korselt criterion for Q( √ −d) (defined in the paper) is of asymptotic density zero.

On Fibonacci numbers which are elliptic Carmichael

Here, we show that if E is a CM elliptic curve with CM field different from Q( √ −1), then the set of n for which the nth Fibonacci number Fn is elliptic Carmichael for E is of asymptotic density zero.

ON r-GENERALIZED FIBONACCI NUMBERS

On Fibonacci Numbers Which Are Powers: I I

where Fm denotes the 77?th Fibonacci number, and o > 1. Without loss of generality , we may require that t be prime. The unique solution for t 2, namely (m, c) = (12, 12)5 was given by J. H. E. Cohn [2], and by 0. Wyler [11]. The unique solution for £ = 3, namely (m9 o) = (6, 2), was given by H. London and R. Finkelstein [5] and by J. C. Lagarias and D. P. Weisser [4]. A. Petho [6] showed that ...