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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.3754","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2013-08-17T05:11:28Z","cross_cats_sorted":[],"title_canon_sha256":"c03b7d9b89abb10d81f66d6b551f36b96ce320b8db9c01bba48e93601b2194b8","abstract_canon_sha256":"8ae03962aea9c9de549da8da2b7760ba9cfbd0623f47b7366f746d83c5f869de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:42.650890Z","signature_b64":"kHjYhaZM8PLzW3dhThcS5EkWXGG056/1SMIGNZFfkebkzx+S4g8bN+Ouse0nMjcuySns3xtiEkXw5fx6DkLiDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62463c5e12f5cb4354b766238db6ef18900b715fa6b172e17454dfe06e2ede0c","last_reissued_at":"2026-05-18T03:15:42.650127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:42.650127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $m$. 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