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bibkey: ordowski2018a126762 authors: Thomas Ordowski year: 2018 title: “OEIS A126762, a(n) is the least k > n such that the remainder when n^k is divided by k is n” doi: null url: https://oeis.org/A126762 claim: “a(n) is the least k > n such that the remainder when n^k is divided by k is n. a(n) is the smallest number k > n such that n^k == n (mod k). Conjecture: a(n) is the smallest number k > n such that n^(k-1) == 1 (mod k). Thus a(n) is coprime to n. - Thomas Ordowski, Aug 03 2018” strata_touched:

  • D5/S0/Certificates/OrdowskiLeastWitnessRefutation license: citation-only triage: anchor

OEIS A126762

Alexander Adamchuk’s name for A126762, dated February 17, 2007, is:

a(n) is the least k > n such that the remainder when n^k is divided by k is n.

Thomas Ordowski’s comment of August 3, 2018 states:

a(n) is the smallest number k > n such that n^k == n (mod k). Conjecture: a(n) is the smallest number k > n such that n^(k-1) == 1 (mod k). Thus a(n) is coprime to n. - Thomas Ordowski, Aug 03 2018

The b-file added in the May 25, 2021 revision contains the line 363 366. Since gcd(363, 366) = 3, this published value already contradicts the coprimality consequence. Exact modular arithmetic at n = 363 shows that the least witness for the defining condition is 366, while 366 does not satisfy the conjectured exponent-shift condition.

The OEIS entry and all 20 revisions, its reverse-reference surface, Crossref, OpenAlex, the MathOverflow API, and GitHub repository, commit, issue, and pull-request searches were checked on September 13, 2026. No proof or refutation was found in the checked surfaces. The arXiv API and HTML surface returned HTTP 429 and were not verified. This bounded search does not assert exhaustive coverage or publication priority.

Verified locator

  • URL: https://oeis.org/A126762
  • NAME (verbatim): a(n) is the least k > n such that the remainder when n^k is divided by k is n.
  • FORMULA conjecture line (verbatim from COMMENTS): a(n) is the smallest number k > n such that n^k == n (mod k). Conjecture: a(n) is the smallest number k > n such that n^(k-1) == 1 (mod k). Thus a(n) is coprime to n. - Thomas Ordowski, Aug 03 2018