{"status": "success", "data": {"description_md": "Let $\\mathcal{S}$ be the set of all ordered pairs $(x,y)$ of positive integers where $xy \\leq  10000$ satisfying\n\n$$\\gcd(x^3,y^3) = 11\\text{ lcm}(x,y) + 3\\gcd(x,y)$$\n\nCompute $|\\mathcal{S}|$ (the size of $\\mathcal{S}$).", "description_html": "<p>Let <span class=\"katex--inline\">\\mathcal{S}</span> be the set of all ordered pairs <span class=\"katex--inline\">(x,y)</span> of positive integers where <span class=\"katex--inline\">xy \\leq  10000</span> satisfying</p>&#10;<p><span class=\"katex--display\">\\gcd(x^3,y^3) = 11\\text{ lcm}(x,y) + 3\\gcd(x,y)</span></p>&#10;<p>Compute <span class=\"katex--inline\">|\\mathcal{S}|</span> (the size of <span class=\"katex--inline\">\\mathcal{S}</span>).</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Holiday Contest 2025 - Team Round - Problem 14", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}