Lucas Primitive Roots
نویسنده
چکیده
is called the characteristic polynomial of the sequence U. In the case where P = -g = 1, the sequence U is the Fibonacci sequence and we denote its terms by F0, Fl9 F2, ... . Let p be an odd prime with p\Q and let e > 1 be an integer. The positive integer u = u(p) is called the rank of apparition of p in the sequence U if p\Uu and p\Um for 0 < m < u; furthermore, u = u(p) is called the period of the sequence U modulo p if it is the smallest positive integer for which U^ E 0 and #fz+l E 1 (mod p) . In the Fibonacci sequence, we denote the rank of apparition of p and period of F modulo p by f(p) and f(p), respectively. Let the number g be a primitive root (mod p). If a? = ̂ satisfies the congruence
منابع مشابه
Products of members of Lucas sequences with indices in an interval being a power
Let r and s be coprime nonzero integers with ∆ = r 2 + 4s = 0. Let α and β be the roots of the quadratic equation x 2 − rx − s = 0, and assume that α/β is not a root of 1. We make the convention that |α| ≥ |β|. Put (u n) n≥0 and (v n) n≥0 for the Lucas sequences of the first and second kind of roots α and β whose general terms are given by
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