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arXiv · 2112.00444

Squares with three digits

Michael Geißer·Theresa Körner·Sascha Kurz·Anne Zahn
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Abstract

We consider integers whose squares have just three decimal digits. Examples are e.g. given by $2108436491907081488939581538^2 = 4445504440405440505004450045555054500055550554550445444$ and $10100000000010401000000000101^2 = 102010000000210100200000110221001000002101002000000010201$. The aim of this paper is to summarize the current knowledge on squares with three digits, scattered around webpages and newsgroup postings, and to add a few new insights. While we will mostly focus on the base $B=10$, several results are presented for general values of $B$. The used mathematical tools are completely elementary. However, we give complete proofs of all statements or explicitly state them as conjectures.

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Michael Geißer, Theresa Körner, Sascha Kurz, Anne Zahn. 2022-01-10. Squares with three digits. https://arxiv.org/abs/2112.00444

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