{"paper":{"title":"A Curious Congruence Involving Alternating Harmonic Sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Liuquan Wang","submitted_at":"2014-07-22T09:04:24Z","abstract_excerpt":"Let $p$ be a prime and ${\\mathcal{P}_{p}}$ the set of positive integers which are prime to $p$. We establish the following interesting congruence \\[\\sum\\limits_{\\begin{smallmatrix}\n  i+j+k={{p}^{r}}\n  i,j,k\\in {\\mathcal{P}_{p}} \\end{smallmatrix}}{\\frac{{{(-1)}^{i}}}{ijk}}\\equiv \\frac{{{p}^{r-1}}}{2}{{B}_{p-3}}\\, (\\bmod \\, {{p}^{r}}).\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5789","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"}