{"paper":{"title":"Squares with three nonzero digits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian-Maria Scheerer, Michael A. Bennett","submitted_at":"2016-10-31T08:56:28Z","abstract_excerpt":"We determine all integers $n$ such that $n^2$ has at most three base-$q$ digits for $q \\in \\{2, 3, 4, 5, 8, 16 \\}$. More generally, we show that all solutions to equations of the shape $$ Y^2 = t^2 + M \\cdot q^m + N \\cdot q^n, $$ where $q$ is an odd prime, $n > m > 0$ and $t^2, |M|, N < q$, either arise from \"obvious\" polynomial families or satisfy $m \\leq 3$. Our arguments rely upon Pad\\'e approximants to the binomial function, considered $q$-adically."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09830","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"}