{"status": "success", "data": {"description_md": "**POTD November 23, 2023**\n**Author:** munch\n\nLet $f: \\mathbb{Z}^+ \\rightarrow \\mathbb{Z}^+$ such that $f(x)$ is the units digit of $x^{(x+1)^{(x+2)^{(x+3)}}}$. Find $\\sum_{x=1}^{100} f(x)$.", "description_html": "<p><strong>POTD November 23, 2023</strong><br/>&#10;<strong>Author:</strong> munch</p>&#10;<p>Let <span class=\"katex--inline\">f: \\mathbb{Z}^+ \\rightarrow \\mathbb{Z}^+</span> such that <span class=\"katex--inline\">f(x)</span> is the units digit of <span class=\"katex--inline\">x^{(x+1)^{(x+2)^{(x+3)}}}</span>. Find <span class=\"katex--inline\">\\sum_{x=1}^{100} f(x)</span>.</p>&#10;", "hints_md": "Try to find patterns for cases of a number $n$ where:\n$n \\equiv 0 \\text{ mod } 10$\n$n \\equiv 1 \\text{ mod } 10$\n$n \\equiv 2 \\text{ mod } 10$\n$\\vdots$\n$n \\equiv 9 \\text{ mod } 10$\n\nFun Fact: The [modpow](https://en.wikipedia.org/wiki/Modular_exponentiation) function and some simple manipulations would (somewhat) trivialize this problem with coding.", "hints_html": "<p>Try to find patterns for cases of a number <span class=\"katex--inline\">n</span> where:<br/>&#10;<span class=\"katex--inline\">n \\equiv 0 \\text{ mod } 10</span><br/>&#10;<span class=\"katex--inline\">n \\equiv 1 \\text{ mod } 10</span><br/>&#10;<span class=\"katex--inline\">n \\equiv 2 \\text{ mod } 10</span><br/>&#10;<span class=\"katex--inline\">\\vdots</span><br/>&#10;<span class=\"katex--inline\">n \\equiv 9 \\text{ mod } 10</span></p>&#10;<p>Fun Fact: The <a href=\"https://en.wikipedia.org/wiki/Modular_exponentiation\">modpow</a> function and some simple manipulations would (somewhat) trivialize this problem with coding.</p>&#10;", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #4", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}