JP Journal of Algebra, Number Theory and Applications
Volume 4, Issue 3, Pages 455 - 463
(December 2004)
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ARITHMETIC
PROPERTIES OF SOME SPECIAL SUMS
Nathan Baxter (U. S. A.) and Mihai Caragiu (U. S. A.)
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Abstract: 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
series and
cannot
be r-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. |
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