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Let $F_{n}$ and $L_n$ be the $n$th Fibonacci number and Lucas number, respectively. The order of appearance of $m$ in the Fibonacci sequence, denoted by $z(m)$, is the smallest positive integer $k$ such that $m$ divides $F_k$. Marques obtained the formula of $z(L_n^k)$ in some cases. In this article, we obtain the formula of $z(L_n^k)$ for all $n, k\geq 1$.
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참고문헌 (8)
참고문헌 신청
B. A. Brousseau / 1972 / Fibonacci and Related Number Theoretic Tables / The Fibonacci Association
J. H. Halton / 1966 / On the divisibility properties of Fibonacci numbers / Fibonacci Quart 4(3):217~240
T. Koshy / 2001 / Fibonacci and Lucas Numbers with Applications / Wiley
T. Lengyel / 1995 / The order of the Fibonacci and Lucas Numbers / Fibonacci Quart 33(3):234~239
D. Marques / 2012 / The order of appearance of powers of Fibonacci and Lucas numbers / Fi-bonacci Quart 50(3):239~245
J. H. Halton / 1966 / On the divisibility properties of Fibonacci numbers / Fibonacci Quart 4(3):217~240
T. Koshy / 2001 / Fibonacci and Lucas Numbers with Applications / Wiley
T. Lengyel / 1995 / The order of the Fibonacci and Lucas Numbers / Fibonacci Quart 33(3):234~239
D. Marques / 2012 / The order of appearance of powers of Fibonacci and Lucas numbers / Fi-bonacci Quart 50(3):239~245
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