On a Generalised Lehmer Problem for Arbitrary Powers
Number Theory
2008-03-27 v2
Abstract
We consider a generalisation of the classical Lehmer problem about the parity distribution of an integer and its modular inverse. We use some known estimates of exponential sums to study a more general question of simultaneous distribution of the residues of any fixed number of negative and positive powers of integers in prescribed arithmetic progressions. In particular, we improve and generalise a recent result of Y. Yi and W. Zhang.
Cite
@article{arxiv.0803.3487,
title = {On a Generalised Lehmer Problem for Arbitrary Powers},
author = {I. E. Shparlinski},
journal= {arXiv preprint arXiv:0803.3487},
year = {2008}
}