{"status": "success", "data": {"description_md": "Let $N$ be the number of subsets $S$ of $\\{1,2,3, \\ldots , 2024\\}$ such that $|S|$ has a remainder of $1$ when divided by $4$. Given that $N$ can be expressed as $a^b$, where $a$ and $b$ are positive integers such that $a$ is prime, find $a+b$. \n\nNote: $|S|$ denotes the number of elements in the set $S$.", "description_html": "<p>Let <span class=\"katex--inline\">N</span> be the number of subsets <span class=\"katex--inline\">S</span> of <span class=\"katex--inline\">\\{1,2,3, \\ldots , 2024\\}</span> such that <span class=\"katex--inline\">|S|</span> has a remainder of <span class=\"katex--inline\">1</span> when divided by <span class=\"katex--inline\">4</span>. Given that <span class=\"katex--inline\">N</span> can be expressed as <span class=\"katex--inline\">a^b</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are positive integers such that <span class=\"katex--inline\">a</span> is prime, find <span class=\"katex--inline\">a+b</span>.</p>&#10;<p>Note: <span class=\"katex--inline\">|S|</span> denotes the number of elements in the set <span class=\"katex--inline\">S</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "TxO Math Bowl 2024 - Individuals B - Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024indivsB-p07", "prev": "/problem/txo2024indivsB-p05"}}