| JP Journal of Algebra, Number Theory and Applications
Volume 4, Issue 3, Pages 455 - 463
PROPERTIES OF SOME SPECIAL SUMS
Nathan Baxter (U. S. A.) and Mihai Caragiu (U. S. A.)
The paper deals with
arithmetic properties of the partial sums of
some special series. We show that if
then the n
-th partial sums of the
-th powers of rational numbers.
Moreover, we show that if
is a sequence of positive rational numbers
such that for every prime p
is not an integer, then
is irrational for all
Several other variations are presented.
|Keywords and phrases: harmonic number, perfect
powers, partial sums, p-adic valuation.