{"status": "success", "data": {"description_md": "**POTD April 1, 2024**\nHappy April Fools! This problem was inspired from China TST.\n\nThe numbers of sequences $(a_1,...,a_{100})$ whose terms are all nonnegative integers less than $97$ such that $97$ divides the sum of all the terms and the sum of the squares of all the terms can be written as $a^b$ where $\\sqrt[n]{a}$ is not an integer for any $n\\ge 2$. Find $a+b$.", "description_html": "<p><strong>POTD April 1, 2024</strong><br/>&#10;Happy April Fools! This problem was inspired from China TST.</p>&#10;<p>The numbers of sequences <span class=\"katex--inline\">(a_1,...,a_{100})</span> whose terms are all nonnegative integers less than <span class=\"katex--inline\">97</span> such that <span class=\"katex--inline\">97</span> divides the sum of all the terms and the sum of the squares of all the terms can be written as <span class=\"katex--inline\">a^b</span> where <span class=\"katex--inline\">\\sqrt[n]{a}</span> is not an integer for any <span class=\"katex--inline\">n\\ge 2</span>. Find <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 10, "problem_name": "Problem of the Day #114", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}