{"status": "success", "data": {"description_md": "Let  $\\mathcal{S}$ be the set of ordered pairs $(a,b)$ such that $a$ and $b$ are positive integers and $$a^2+7a+26=ab+2b. $$\n\nFind $$\\sum_{(a,b) \\in \\mathcal{S}} (a+b). $$", "description_html": "<p>Let  <span class=\"katex--inline\">\\mathcal{S}</span> be the set of ordered pairs <span class=\"katex--inline\">(a,b)</span> such that <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are positive integers and <span class=\"katex--display\">a^2+7a+26=ab+2b.</span></p>&#10;<p>Find <span class=\"katex--display\">\\sum_{(a,b) \\in \\mathcal{S}} (a+b).</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p19", "prev": "/problem/txo2024team-p17"}}