{"status": "success", "data": {"description_md": "Let $F_n$ be defined recursively such that $F_n = F_{n - 1} + F_{n - 2}$ (the Fibonacci sequence), and $F_1 = F_2 = 1$.\n\nNow define $S_n$ such that: $$ S_n= \\sum\\limits_{i = 1}^{n}F_i^2 $$\n\nFind the least $n$ such that $100 \\mid S_n$.", "description_html": "<p>Let <span class=\"katex--inline\">F_n</span> be defined recursively such that <span class=\"katex--inline\">F_n = F_{n - 1} + F_{n - 2}</span> (the Fibonacci sequence), and <span class=\"katex--inline\">F_1 = F_2 = 1</span>.</p>&#10;<p>Now define <span class=\"katex--inline\">S_n</span> such that: <span class=\"katex--display\"> S_n= \\sum\\limits_{i = 1}^{n}F_i^2</span></p>&#10;<p>Find the least <span class=\"katex--inline\">n</span> such that <span class=\"katex--inline\">100 \\mid S_n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "TxO Math Bowl 2024 - Individuals A - Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024indivsA-p13", "prev": "/problem/txo2024indivsA-p11"}}