{"paper":{"title":"On the difference between a D. H. Lehmer number and its inverse over short interval","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Haodong Wang, Rong Ma, Yana Niu","submitted_at":"2021-04-01T03:00:38Z","abstract_excerpt":"Let $q>2$ be an odd integer. For each integer $x$ with $0<x<q$ and $(q,x)= 1$, we know that there exists one and only one $\\bar{x}$ with $0<\\bar{x}<q$ such that $x\\bar{x}\\equiv1(\\bmod q)$. A Lehmer number is defined to be any integer $a$ with $2\\dagger(a+\\bar{a})$. For any nonnegative integer $k$, Let $$ M(x,q,k)=\\displaystyle\\mathop {\\displaystyle\\mathop{\\sum{'}}_{a=1}^{q} \\displaystyle\\mathop{\\sum{'}}_{b\\leq xq}}_{\\mbox{$\\tiny\\begin{array}{c} 2|a+b+1\\\\ ab\\equiv1(\\bmod q)\\end{array}$}}(a-b)^{2k}.$$ The main purpose of this paper is to study the properties of $M(x,q,k)$, and give a sharp asymp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.00216","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.00216/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}