{"paper":{"title":"Some results on natural numbers represented by quadratic polynomials in two variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B. M. Cerna Magui\\~na, H. Blas, V. H. L\\'opez Sol\\'is","submitted_at":"2018-08-18T23:13:04Z","abstract_excerpt":"We consider a set of equations of the form $p_j (x,y) = (10 x+m_j)(10 y + n_j),\\,\\,x\\geq 0, y\\geq0$, $j=1,2,3$, such that $\\{m_1=7, n_1=3\\}$, $\\{m_2=n_2=9\\}$ and $\\{m_3=n_3=1\\}$, respectively. It is shown that if $(a(p_j),b(p_j)) \\in N \\times N$ is a solution of the $j'$th equation one has the inequality $\\frac{p_j}{100}\\leq A(p_j) B(p_j) \\leq \\frac{121}{10^4} p_j$, where $A(p_j)\\equiv a(p_j)+1, B(p_j)\\equiv b(p_j)+1\\,$ and $p_{j}$ is a natural number ending in 1, such that $\\{A(p_1)\\geq 4, B(p_1)\\geq 8\\}$, $\\{A(p_2) \\geq 2, B(p_2)\\geq 2\\}$, and $\\{A(p_3) \\geq 10, B(p_3)\\geq 10\\}$ hold, respec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06145","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"}