{"status": "success", "data": {"description_md": "Let $f\\colon \\mathbb{Z^+} \\rightarrow \\mathbb{Z^+}$ be a function satisfying $f(x)=x^4+6x^2+2x-5$. Let $S$ be the sum of all positive integers $n$ such that $f(n)$ is a perfect square. What is the sum of the digits of $S^2$?\n\n$\\textbf{(A)}~1\\qquad \\textbf{(B)}~10\\qquad\\textbf{(C)}~11\\qquad\\textbf{(D)}~13\\qquad\\textbf{(E)}~16$", "description_html": "<p>Let <span class=\"katex--inline\">f\\colon \\mathbb{Z^+} \\rightarrow \\mathbb{Z^+}</span> be a function satisfying <span class=\"katex--inline\">f(x)=x^4+6x^2+2x-5</span>. Let <span class=\"katex--inline\">S</span> be the sum of all positive integers <span class=\"katex--inline\">n</span> such that <span class=\"katex--inline\">f(n)</span> is a perfect square. What is the sum of the digits of <span class=\"katex--inline\">S^2</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}~1\\qquad \\textbf{(B)}~10\\qquad\\textbf{(C)}~11\\qquad\\textbf{(D)}~13\\qquad\\textbf{(E)}~16</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2024 Mock AMC 12 - Problem 21", "can_next": true, "can_prev": true, "nxt": "/problem/2024_mock_amc12-p22", "prev": "/problem/2024_mock_amc12-p20"}}