Sums of the Form 1/x_1^k + ... + 1/x_n^k Modulo a Prime

Details Sums of the Form 1/x_1^k + ... + 1/x_n^k Modulo a Prime Sums of the Form 1/x_1^k + ... + 1/x_n^k Modulo a Prime

2004-03-22

arxiv.org/abs/math/0403360v2

Mathematics

Number Theory

Light Corrections. The parameter h in the definition of T had to be a lot larger

Scientific paper

We show that for every $0 < \epsilon \leq 1$ and integer $k\geq 1$, there
exists an integer $n = n(\epsilon,k)$ so that for all primes $p$, and integers
$0 \leq a \leq p-1$, there exist integers $1 \leq x_1 < ... < x_n \leq
p^\epsilon$ such that $a \equiv x_1^{-1} + ... + x_n^{-1} \pmod{p}$. This
extends a result of I. Shparlinski.

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