{"status": "success", "data": {"description_md": "How many positive integer pairs $(x, y)$ exist, where $x \\leq 20$ and $y \\leq 20$, such that $$ \\sin\\left(\\frac{\\pi x^2}{2}\\right)\\cos\\left(\\frac{\\pi y^2}{2}\\right) = -1.$$", "description_html": "<p>How many positive integer pairs <span class=\"katex--inline\">(x, y)</span> exist, where <span class=\"katex--inline\">x \\leq 20</span> and <span class=\"katex--inline\">y \\leq 20</span>, such that <span class=\"katex--display\"> \\sin\\left(\\frac{\\pi x^2}{2}\\right)\\cos\\left(\\frac{\\pi y^2}{2}\\right) = -1.</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Holiday Contest 2025 - Guts Round - Set 5 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}