{"status": "success", "data": {"description_md": "What is the greatest power of $2$ that is a factor of $10^{1002} - 4^{501}$?\n\n$\\textbf{(A) } 2^{1002} \\qquad\\textbf{(B) } 2^{1003} \\qquad\\textbf{(C) } 2^{1004} \\qquad\\textbf{(D) } 2^{1005} \\qquad\\textbf{(E) }2^{1006}$", "description_html": "<p>What is the greatest power of  <span class=\"katex--inline\">2</span>  that is a factor of  <span class=\"katex--inline\">10^{1002} - 4^{501}</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 2^{1002} \\qquad\\textbf{(B) } 2^{1003} \\qquad\\textbf{(C) } 2^{1004} \\qquad\\textbf{(D) } 2^{1005} \\qquad\\textbf{(E) }2^{1006}</span> </p>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2014 AMC 10B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc10B_p18", "prev": "/problem/14_amc10B_p16"}}