{"status": "success", "data": {"description_md": "**POTD May 19, 2024**\n\nLet $f(x)$ return the smallest positive integer $n$, such that $n \\geq x$, and the digit sums of $n$ and $2n$ are perfect squares. If $\\prod\\limits_{k=1}^{90}f(k)$ can be expressed as $a^b \\cdot (c!)^d$, where $a$, $b$, $c$, and $d$ are positive integers, and $a$ is a prime number, find $a+b+c+d$.", "description_html": "<p><strong>POTD May 19, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">f(x)</span> return the smallest positive integer <span class=\"katex--inline\">n</span>, such that <span class=\"katex--inline\">n \\geq x</span>, and the digit sums of <span class=\"katex--inline\">n</span> and <span class=\"katex--inline\">2n</span> are perfect squares. If <span class=\"katex--inline\">\\prod\\limits_{k=1}^{90}f(k)</span> can be expressed as <span class=\"katex--inline\">a^b \\cdot (c!)^d</span>, where <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, <span class=\"katex--inline\">c</span>, and <span class=\"katex--inline\">d</span> are positive integers, and <span class=\"katex--inline\">a</span> is a prime number, find <span class=\"katex--inline\">a+b+c+d</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #161", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}