The aim of this paper is to give new results about factorizations of the Fibonacci numbers F n and the Lucas numbers L n. These numbers are defined by the second order recurrence relation a n+2 = a n+1+a n with the initial terms F 0 = 0, F 1 = 1 and L 0 = 2, L 1 = 1, respectively. Proofs of theorems are done with the help of connections between determinants of tridiagonal matrices and the Fibonacci and the Lucas numbers using the Chebyshev polynomials. This method extends the approach used in [CAHILL, N. D.a€”Da€?ERRICO, J. R.a€”SPENCE, J. P.: Complex factorizations of the Fibonacci and Lucas numbers, Fibonacci Quart. 41 (2003), 13-19], and CAHILL, N. D.a€”NARAYAN, D. A.: Fibonacci and Lucas numbers as tridiagonal matrix determinants, Fibonacci Quart. 42 (2004), 216-221].
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机译：本文的目的是给出有关斐波那契数F n和卢卡斯数L n分解的新结果。这些数字由二阶递归关系a n + 2 = a n + 1 + a n定义，初始项分别为F 0 = 0，F 1 = 1和L 0 = 2，L 1 = 1。定理的证明是通过使用Chebyshev多项式在三对角矩阵的行列式与Fibonacci和Lucas数之间的联系来完成的。该方法扩展了[CAHILL，N.D.Darrerico，J.R.a€” SPENCE，J.P。：Fibonacci和Lucas数的复杂因式分解，Fibonacci Quart。 41（2003），13-19]，和CAHILL，N. D.a.“ NARAYAN，D. A .: Fibonacci和Lucas数作为三对角矩阵的决定因素，Fibonacci Quart。 42（2004），216-221]。
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