The 2-adic valuation of generalized Fibonacci sequences with an application to certain Diophantine equations
نویسندگان
چکیده
منابع مشابه
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 one-dimensional quasilattices L lying in the square Fibonacci quasilattice F2 = F×F are classified; here F is the one-dimensional Fibonacci quasilattice. It is proved that there exists a countable set of similarity classes of quasilattices L in F2 (fine classification), and also four classes of local equivalence (rough classification). Asymptotic distributions of points in quasilattices L a...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2017
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2017.06.008