  Let $n$ be a positive integer. In 1915, Theisinger proved that if $n\ge 2$,
then the $n$-th harmonic sum $\sum_{k=1}^n\frac{1}{k}$ is not an integer. Let
$a$ and $b$ be positive integers. In 1923, Nagell extended Theisinger's theorem
by showing that the reciprocal sum $\sum_{k=1}^{n}\frac{1}{a+(k-1)b}$ is not an
integer if $n\ge 2$. In 1946, Erd\H{o}s and Niven proved a theorem of a similar
nature that states that there is only a finite number of integers $n$ for which
one or more of the elementary symmetric functions of $1,1/2, ..., 1/n$ is an
integer. In this paper, we present a generalization of Nagell's theorem. In
fact, we show that for arbitrary $n$ positive integers $s_1, ..., s_n$ (not
necessarily distinct and not necessarily monotonic), the following reciprocal
power sum $$\sum\limits_{k=1}^{n}\frac{1}{(a+(k-1)b)^{s_{k}}}$$ is never an
integer if $n\ge 2$. The proof of our result is analytic and $p$-adic in
character.
