{"paper":{"title":"On inequality $|z^n-1|\\geq|z-1|$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Rados Bakic","submitted_at":"2014-06-04T08:41:33Z","abstract_excerpt":"It is known that inequality $|z^n-1|\\geq|z-1|$ holds on the circle $|z-1/2|= 1/2$, where $n$ is a positive integer. We prove that in fact $n$ can be real number not less then 1. We also prove following inequality as a lemma: $cos^nx\\lt 1-sinx$ for real $n\\gt3$ and $2\\pi/(n+1)\\leq x \\lt \\pi/2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1166","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"}