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arXiv · 0704.1327

On the largest prime factor of the Mersenne numbers

Kevin Ford·Florian Luca·Igor E. Shparlinski
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Abstract

Let P(k) be the largest prime factor of the positive integer k. In this paper, we prove that the series $\sum_{n\ge 1}\frac{(\log n)^a}{P(2^n-1)}$ is convergent for each constant a<1/2, which gives a more precise form of a result of C. L. Stewart from 1977.

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Kevin Ford, Florian Luca, Igor E. Shparlinski. 2007-04-10. On the largest prime factor of the Mersenne numbers. https://arxiv.org/abs/0704.1327

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