On integer parts of the reciprocal remainders of some sums.

We present generalizations of some results on the integer parts of the reciprocal remainders of the zeta function ζ (s) with s = 2 and s = 3 , and a very short and elegant proof of a recent result on the integer parts of the reciprocal remainders of the series ζ (3) . We also give some historical and theoretical remarks to problems of this type, conduct some analyses, and make some connections with the theory of linear difference equations with constant coefficients. [ABSTRACT FROM AUTHOR]