Elementary Proof of the Completeness of OEIS A051221 Below 2000 https://arxiv.org/abs/2504.00116 #mathNT
The OEIS sequence A051221 consists of nonnegative integers of the form 10^x - y^2. The known values are those less than or equal to 2000 with x <= 7, and it is conjectured that no new values in this range appear for x >= 8. In this paper, we give an elementary proof that this is indeed the case by using Pell-type equations.
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