Theory of Binet formulas for Fibonacci and Lucas p-numbers

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On generalized Fibonacci and Lucas polynomials (2009, background): “Introduction In modern science there is a huge interest in the theory and application of the Golden Section and Fibonacci numbers [1–34].”
On the Fibonacci k-numbers (2007, background): “In the present days there is a huge interest of modern science in the application of the Golden Section and Fibonacci numbers [1–19].”
The k-Fibonacci sequence and the Pascal 2-triangle (2007, background): “Binet’s formulas are well known in the Fibonacci numbers theory [1,12].”
On the m-extension of the Fibonacci and Lucas p-numbers (2009, unknown): “Stakhov and Rozin’s researches [11–14] complete a theory of the Fibonacci p-numbers, give a general theory of the ‘‘golden’’ algebraic equations [11], introduce the generalized Binet formula for the Fibonacci p-numbers and introduce the generalized Lucas p-numbers [12] that are given by the followin”
On k-Fibonacci sequences and polynomials and their derivatives (2009, background): “The well-known Binet’s formula in the Fibonacci numbers theory [1,8,21] allows us to express the k-Fibonacci number in function of the roots r1 and r2 of the characteristic equation, associated to the recurrence relation (1) r(2) = kr + 1: F k;n 1⁄4 r1 r2 r1 r2 ð3Þ If r denotes the positive root of ”