Elementary Proof of the Completeness of OEIS A051221 Below 2000
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913769173549056 |
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| author | Azuma, Seiichi |
| author_facet | Azuma, Seiichi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00116 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elementary Proof of the Completeness of OEIS A051221 Below 2000 Azuma, Seiichi Number Theory 11Y50 (Primary), 11D09, 11Y55 (Secondary) 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. |
| title | Elementary Proof of the Completeness of OEIS A051221 Below 2000 |
| topic | Number Theory 11Y50 (Primary), 11D09, 11Y55 (Secondary) |
| url | https://arxiv.org/abs/2504.00116 |