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