Squares with three digits

Titelangaben

Geißer, Michael ; Körner, Theresa ; Kurz, Sascha ; Zahn, Anne:
Squares with three digits.
Bayreuth , 2022 . - 42 S.

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Abstract

We consider integers whose squares have just three decimal digits. Examples are e.g. given by 2108436491907081488939581538² = 4445504440405440505004450045555054500055550554550445444 and 10100000000010401000000000101² = 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.