Conditions for the Existence of Generalized Fibonacci Primitive Roots
نویسنده
چکیده
Consider sequences of integers {Un}TM=0 defined by U„ = aUn_x +bUn_2 for all integers n > 2, where U0 = 0, C/j = 1, a and b are given integers. We call these sequences generalized Fibonacci sequences with parameters a and b. In the case where a = b = 1, the sequence {Un}TM=0 is called the Fibonacci sequence, and we denote its terms by F0,Fl9.... The polynomial f(x) = x-ax-h with discriminant D = a+4h is called the characteristic polynomial of the sequence {Un}^0. Suppose that / (x) = 0 has two distinct solutions crand/?. Then we can express U„ in the Binetform,
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