{"paper":{"title":"Some Arithmetic Properties of the q-Euler Numbers and q-Sali\\'e Numbers","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiang Zeng, Victor J. W. Guo","submitted_at":"2005-04-28T12:56:42Z","abstract_excerpt":"For m>n\\geq 0 and 1\\leq d\\leq m, it is shown that the q-Euler number E_{2m}(q) is congruent to q^{m-n}E_{2n}(q) mod (1+q^d) if and only if m\\equiv n mod d. The q-Sali\\'e number S_{2n}(q) is shown to be divisible by (1+q^{2r+1})^{\\left\\lfloor \\frac{n}{2r+1}\\right\\rfloor} for any r\\geq 0. Furthermore, similar congruences for the generalized q-Euler numbers are also obtained, and some conjectures are formulated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504569","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}