{"paper":{"title":"The plastic number and its generalized polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Vasileios Iliopoulos","submitted_at":"2014-07-08T14:05:28Z","abstract_excerpt":"The polynomial $X^{3}-X-1$ has a unique positive root known as plastic number, which is denoted by $\\rho$ and is approximately equal to $1.32471795$. In this note we study the zeroes of the generalized polynomial $X^{k}-\\sum_{j=0}^{k-2}X^{j}$ for $k\\geq 3$ and prove that its unique positive root $\\lambda_{k}$ tends to the golden ratio $\\phi=\\frac{1+\\sqrt{5}}{2}$ as $k \\to \\infty$. We also derive bounds on $\\lambda_{k}$ in terms of Fibonacci numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2091","kind":"arxiv","version":3},"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"}