{"status": "success", "data": {"description_md": "**POTD June 26, 2024**\n\nIt is a well known fact that powers of $2\\text{ mod }10$ are cyclic with a period of $4$. A lesser known fact is that powers of $2\\text{ mod }100$ and $2\\text{ mod }1000$ are also cyclic, with periods of $20$ and $100$, respectively. Find (try to prove it!) the period of the cyclic powers of $2\\text{ mod }10^8$.", "description_html": "<p><strong>POTD June 26, 2024</strong></p>&#10;<p>It is a well known fact that powers of <span class=\"katex--inline\">2\\text{ mod }10</span> are cyclic with a period of <span class=\"katex--inline\">4</span>. A lesser known fact is that powers of <span class=\"katex--inline\">2\\text{ mod }100</span> and <span class=\"katex--inline\">2\\text{ mod }1000</span> are also cyclic, with periods of <span class=\"katex--inline\">20</span> and <span class=\"katex--inline\">100</span>, respectively. Find (try to prove it!) the period of the cyclic powers of <span class=\"katex--inline\">2\\text{ mod }10^8</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "Problem of the Day #199", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}