The order of appearance of the product of five consecutive Lucas numbers

In: Tatra Mountains Mathematical Publications, vol. 59, no. 2

Diego Marques - Pavel Trojovský

Detaily:

Rok, strany: 2014, 65 - 77

Kľúčové slová:

Fibonacci numbers, Lucas numbers, order of appearance, $p$-adic order

O článku:

Let $ F_n$ be the $n$th Fibonacci number and let $L_n$ be the $n$th Lucas number. The order of appearance $z(n)$ of a natural number $n$ is defined as the smallest natural number $k$ such that $n$ divides $F_k$. For instance, $z(F_n)=n=z(L_n)/2$ for all $n>2$. In this paper, among other things, we prove that

$$ z(L_nL_n+1L_n+2L_n+3L_n+4)=\dfrac{n(n+1)(n+2)(n+3)(n+4)}{12} $$

for all positive integers $n\equiv 0,8\pmod{12}$.

Ako citovať:

ISO 690:

Marques, D., Trojovský, P. 2014. The order of appearance of the product of five consecutive Lucas numbers. In Tatra Mountains Mathematical Publications, vol. 59, no.2, pp. 65-77. 1210-3195.

APA:

Marques, D., Trojovský, P. (2014). The order of appearance of the product of five consecutive Lucas numbers. Tatra Mountains Mathematical Publications, 59(2), 65-77. 1210-3195.