{"paper":{"title":"Discriminators of quadratic polynomials","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Soohyun Park","submitted_at":"2013-08-17T05:11:28Z","abstract_excerpt":"Given $f \\in \\mathbb{Z}[x]$ and $n \\in \\mathbb{Z^{+}}$, the $\\emph{discriminator}$ $D_f(n)$ is the smallest positive integer $m$ such that $f(1), \\ldots, f(n)$ are distinct mod $m$. In a recent paper, Z.-W. Sun proved that $D_f(n) = d^{\\lceil \\log_d n \\rceil}$ if $f(x) = x(dx - 1)$ for $d \\in \\{2, 3\\}$. We extend this result to $d = 2^r$ for any $r \\in \\mathbb{Z}^{+}$ and find that $D_f(n) = 2^{\\lceil \\log_2 n \\rceil}$ in this case. We also provide more general statements for $d = p^r$, where $p$ is a prime. In addition, we present a potential method for generating prime numbers with discrimin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3754","kind":"arxiv","version":1},"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"}