{"paper":{"title":"On the modular Erd\\H{o}s-Burgess constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Haoli Wang, Jun Hao, Lizhen Zhang","submitted_at":"2018-07-19T07:10:50Z","abstract_excerpt":"Let $n$ be a positive integer. For any integer $a$, we say that $a$ is idempotent modulo $n$ if $a^2\\equiv a\\pmod n$. The $n$-modular Erd\\H{o}s-Burgess constant is the smallest positive integer $\\ell$ such that any $\\ell$ integers contain one or more integers whose product is idempotent modulo $n$. We gave a sharp lower bound of the $n$-modular Erd\\H{o}s-Burgess constant, in particular, we determined the $n$-modular Erd\\H{o}s-Burgess constant in the case when $n$ is a prime power or a product of pairwise distinct primes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07266","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"}