2021/12/01 by Geißer, Michael, Körner, Theresa, Kurz, Sascha +1
#00A08 #11A63 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2112.00444
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.