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arXiv · 2511.15850

Elementary Bounds on Digital Sums of Powers, Factorials, and LCMs

David G. Radcliffe
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Abstract

We prove logarithmic lower bounds on digital sums of powers, multiples of powers, factorials, and the least common multiple of $\{1,\ldots, n\}$, using only elementary number theory. We conclude with an expository proof of Stewart's theorem on digital sums of powers, which uses Baker's theorem on linear forms in logarithms.

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David G. Radcliffe. 2025-11-19. Elementary Bounds on Digital Sums of Powers, Factorials, and LCMs. https://arxiv.org/abs/2511.15850

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