Quadratic Reciprocity via Lucas Sequences
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p-ADIC CONGRUENCES FOR GENERALIZED FIBONACCI SEQUENCES
is the ordinary formal power series generating function for the sequence {yn+i}„>0 (cf. [12]. Furthermore, it is easy to see [1] that when the discriminant A = X +4ju ofP(t) is nonnegative and X & 0, the ratios yn+l I yn converge (in the usual archimedean metric on U) to a reciprocal root a of P(t). In this article we show that ratios of these y n also exhibit rapid convergence properties relat...
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The Biquadratic Reciprocity Law is used to produce a deterministic primality test for Gaussian Mersenne norms which is analogous to the Lucas–Lehmer test for Mersenne numbers. It is shown that the proposed test could not have been obtained from the Quadratic Reciprocity Law and Proth’s Theorem. Other properties of Gaussian Mersenne norms that contribute to the search for large primes are given....
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تاریخ انتشار 1993