{"paper":{"title":"The generalized Pillai equation $\\pm r a^x \\pm s b^y = c$, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Reese Scott, Robert Styer","submitted_at":"2011-02-22T03:18:42Z","abstract_excerpt":"We consider $N$, the number of solutions $(x,y,u,v)$ to the equation $ (-1)^u r a^x + (-1)^v s b^y = c $ in nonnegative integers $x, y$ and integers $u, v \\in \\{0,1\\}$, for given integers $a>1$, $b>1$, $c>0$, $r>0$ and $s>0$. When $(ra,sb)=1$, we show that $N \\le 3$ except for a finite number of cases all of which satisfy $\\max(a,b,r,s, x,y) < 2 \\cdot 10^{15}$ for each solution; when $(a,b)>1$, we show that $N \\le 3$ except for three infinite families of exceptional cases. We find several different ways to generate an infinite number of infinite families of cases giving N=3 solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4833","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"}