TL;DR
This paper provides an alternative proof and improvements to recent results on the distribution of multiplicative inverses within short intervals, focusing on interval spacing conditions.
Contribution
It offers a new proof method and enhances existing bounds for multiplicative inverses in short intervals under specific spacing assumptions.
Findings
Improved bounds on multiplicative inverses in short intervals.
Extended results under additional spacing conditions.
Alternative proof technique for existing theorems.
Abstract
We give an alternative proof of a recent result by T.D. Browning and A. Haynes (arXiv:1204.6374v1) on multiplicative inverses in sequences of intervals and improve this result under additional conditions on the spacing of these intervals.
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