{"paper":{"title":"A note on Linnik's Theorem on quadratic non-residues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"B\\'ela Bollob\\'as, Jonathan D. Lee, Oliver Riordan, Paul Balister, Robert Morris","submitted_at":"2017-12-19T19:53:12Z","abstract_excerpt":"We present a short, self-contained, and purely combinatorial proof of Linnik's theorem: for any $\\varepsilon > 0$ there exists a constant $C_\\varepsilon$ such that for any $N$, there are at most $C_\\varepsilon$ primes $p \\leqslant N$ such that the least positive quadratic non-residue modulo $p$ exceeds $N^\\varepsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07179","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"}