{"status": "success", "data": {"description_md": "An integer $N$ is selected at random in the range $1\\leq N \\leq 2020$. What is the probability that the remainder when $N^{16}$ is divided by $5$ is $1$?\n\n$\\textbf{(A)}\\ \\frac{1}{5}\\qquad\\textbf{(B)}\\ \\frac{2}{5}\\qquad\\textbf{(C)}\\ \\frac{3}{5}\\qquad\\textbf{(D)}\\ \\frac{4}{5}\\qquad\\textbf{(E)}\\ 1$", "description_html": "<p>An integer  <span class=\"katex--inline\">N</span>  is selected at random in the range  <span class=\"katex--inline\">1\\leq N \\leq 2020</span> . What is the probability that the remainder when  <span class=\"katex--inline\">N^{16}</span>  is divided by  <span class=\"katex--inline\">5</span>  is  <span class=\"katex--inline\">1</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{1}{5}\\qquad\\textbf{(B)}\\ \\frac{2}{5}\\qquad\\textbf{(C)}\\ \\frac{3}{5}\\qquad\\textbf{(D)}\\ \\frac{4}{5}\\qquad\\textbf{(E)}\\ 1</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": "2017 AMC 10B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc10B_p15", "prev": "/problem/17_amc10B_p13"}}