Riv.Mat.Univ.Parma (6) 3 (2000)


On the difference of perfect powers and sums of terms of linear recurrences

Pages: 77-85
Received: 3 March 2000   
Mathematics Subject Classification (2000): 11B39 - 11J86

Work partially supported by the Hungarian OTKA Foundation, No. T 032898

Abstract: Let G(i) = {Gx(i)} ¥x=0 (i=1,2, ..., m; m³2) be linear sequences of order ki³2 and Gx(i)ÎZ. Let K>1 be a fixed real number and

S={sÎZ : s = ±p1e1 ... prer, ei Î N }, where pi's are fixed primes. In this paper under some restrictions, it is proved that, if x1>K max2£ i£m(xi) then there exists a positive constant c such that ||swq| - |åm i=1 Gxi(i)||>ecx1 holds for any positive integers w³2, x1 > x0, x 2, ..., xm, q>q0 and sÎ S, where x0, c and q0 are effectively computable positive constants depending on K, S and the sequences G(i).

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