论文标题
普遍的斐波那契多项式的不可约性
Irreducibility of generalized Fibonacci polynomials
论文作者
论文摘要
如果二阶多项式序列为fibonacci-type $ \ MATHCAL {f} _ {n} $（Lucas-Type $ \ Mathcal {L} _ {n} $），如果其Binet公式的结构与fibonacci（Lucas（Lucas））相似。在某些条件下，当且仅当$ n $是质量数字时，这些多项式是不可约的。例如，斐波那契多项式，pell多项式，费玛（Fermat）多项式，卢卡斯多项式，pell-lucas多项式，fermat-lucas多项式在$ n $时是不可修复的；和Chebyshev多项式（第二类），Morgan-Voyce多项式（斐波那契型）和越野多项式时，当$ n $是质量时，可以还原。 在本文中，我们给出一些定理，以确定fibonacci型多项式和卢卡斯型多项式是不可约时的。
A second order polynomial sequence is of Fibonacci-type $\mathcal{F}_{n}$ (Lucas-type $\mathcal{L}_{n}$) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Under certain conditions these polynomials are irreducible if and only if $n$ is a prime number. For example, the Fibonacci polynomials, Pell polynomials, Fermat polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials are irreducible when $n$ is a prime number; and Chebyshev polynomials (second kind), Morgan-Voyce polynomials (Fibonacci type), and Vieta polynomials are reducible when $n$ is a prime number. In this paper we give some theorems to determine whether the Fibonacci type polynomials and Lucas type polynomials are irreducible when $n$ is prime.
