Elementary Bounds on Digital Sums of Powers, Factorials, and LCMs
Number Theory
2026-01-09 v2
Abstract
We prove logarithmic lower bounds on digital sums of powers, multiples of powers, factorials, and the least common multiple of , 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.
Cite
@article{arxiv.2511.15850,
title = {Elementary Bounds on Digital Sums of Powers, Factorials, and LCMs},
author = {David G. Radcliffe},
journal= {arXiv preprint arXiv:2511.15850},
year = {2026}
}
Comments
15 pages, 3 figures. This version corrects errors in the earlier manuscript and substantially clarifies the arguments by adding detailed explanations and additional figures