论文标题
Zeckendorf乘法倒置的表示模式A fibonacci编号
Zeckendorf representation of multiplicative inverses modulo a Fibonacci number
论文作者
论文摘要
PremPreesuk，Noppakaew和Pongsriiam确定了Zeckendorf的Zeckendorf代表乘以$ 2 $ MODULO $ f_n $的Zeckendorf表示，对于每个正整数$ n $不可划分的$ 3 $，其中$ f_n $表示$ n $ n $ n $ n $ th fibonacci编号。我们确定$ a $ a $ modulo $ f_n $的乘法倒数的zeckendorf表示，对于每个固定整数$ a \ geq 3 $，对于所有正整数$ n $，带有$ \ gcd（a，f_n）= 1 $。我们的证明利用了所谓的基础-UM $φ$扩展实数。
Prempreesuk, Noppakaew, and Pongsriiam determined the Zeckendorf representation of the multiplicative inverse of $2$ modulo $F_n$, for every positive integer $n$ not divisible by $3$, where $F_n$ denotes the $n$th Fibonacci number. We determine the Zeckendorf representation of the multiplicative inverse of $a$ modulo $F_n$, for every fixed integer $a \geq 3$ and for all positive integers $n$ with $\gcd(a, F_n) = 1$. Our proof makes use of the so-called base-$φ$ expansion of real numbers.
