{"status": "success", "data": {"description_md": "Let $a_1,a_2,\\dots,a_{2018}$ be a strictly increasing sequence of positive integers such that $$a_1+a_2+\\cdots+a_{2018}=2018^{2018}.$$ What is the remainder when $a_1^3+a_2^3+\\cdots+a_{2018}^3$ is divided by $6$?\n\n$\\textbf{(A) }0 \\qquad\n\\textbf{(B) }1 \\qquad\n\\textbf{(C) }2 \\qquad\n\\textbf{(D) }3 \\qquad\n\\textbf{(E) }4 \\qquad$", "description_html": "<p>Let  <span class=\"katex--inline\">a_1,a_2,\\dots,a_{2018}</span>  be a strictly increasing sequence of positive integers such that  <span class=\"katex--display\">a_1+a_2+\\cdots+a_{2018}=2018^{2018}.</span>  What is the remainder when  <span class=\"katex--inline\">a_1^3+a_2^3+\\cdots+a_{2018}^3</span>  is divided by  <span class=\"katex--inline\">6</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) }0 \\qquad\n\\textbf{(B) }1 \\qquad\n\\textbf{(C) }2 \\qquad\n\\textbf{(D) }3 \\qquad\n\\textbf{(E) }4 \\qquad</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": "2018 AMC 10B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10B_p17", "prev": "/problem/18_amc10B_p15"}}