{"paper":{"title":"Some subgroups of a finite field and their applications for obtaining explicit factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Manjit Singh","submitted_at":"2018-06-27T03:04:30Z","abstract_excerpt":"Let $\\mathcal{S}_q$ denote the group of all square elements in the multiplicative group $\\mathbb{F}_q^*$ of a finite field $\\mathbb{F}_q$ of odd characteristic containing $q$ elements. Let $\\mathcal{O}_q$ be the set of all odd order elements of $\\mathbb{F}_q^*$. Then $\\mathcal{O}_q$ turns up as a subgroup of $\\mathcal{S}_q$. In this paper, we show that $\\mathcal{O}_q=\\langle4\\rangle$ if $q=2t+1$ and, $\\mathcal{O}_q=\\langle t\\rangle $ if $q=4t+1$, where $q$ and $t$ are odd primes. This paper also gives a direct method for obtaining the coefficients of irreducible factors of $x^{2^nt}-1$ in $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.11052","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"}