On a Generalised Lehmer Problem for Arbitrary Powers

Details On a Generalised Lehmer Problem for Arbitrary Powers On a Generalised Lehmer Problem for Arbitrary Powers

2008-03-25

arxiv.org/abs/0803.3487v2

Mathematics

Number Theory

Scientific paper

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.

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