{"status": "success", "data": {"description_md": "Let $a > 0$, and let $P(x)$ be a polynomial with integer coefficients such that\n$$P(1) = P(3) = P(5) = P(7) = a$$, and<br/>\n$$P(2) = P(4) = P(6) = P(8) = -a.$$\nWhat is the smallest possible value of $a$?\n\n$\\textbf{(A)}\\ 105 \\qquad \\textbf{(B)}\\ 315 \\qquad \\textbf{(C)}\\ 945 \\qquad \\textbf{(D)}\\ 7! \\qquad \\textbf{(E)}\\ 8!$", "description_html": "<p>Let <span class=\"katex--inline\">a &gt; 0</span>, and let <span class=\"katex--inline\">P(x)</span> be a polynomial with integer coefficients such that<br/>&#10;<span class=\"katex--display\">P(1) = P(3) = P(5) = P(7) = a</span>, and<br/><br/>&#10;<span class=\"katex--display\">P(2) = P(4) = P(6) = P(8) = -a.</span><br/>&#10;What is the smallest possible value of <span class=\"katex--inline\">a</span>?</p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 105 \\qquad \\textbf{(B)}\\ 315 \\qquad \\textbf{(C)}\\ 945 \\qquad \\textbf{(D)}\\ 7! \\qquad \\textbf{(E)}\\ 8!</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2010 AMC 10B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/10_amc10B_p24"}}