{"status": "success", "data": {"description_md": "If the positive integer $c$ has positive integer divisors $a$ and $b$ with $c = ab$, then $a$ and $b$ are said to be $\\textit{complementary}$ divisors of $c$. Suppose that $N$ is a positive integer that has one complementary pair of divisors that differ by $20$ and another pair of complementary divisors that differ by $23$. What is the sum of the digits of $N$?\n\n$\\textbf{(A) } 9 \\qquad \\textbf{(B) } 13\\qquad \\textbf{(C) } 15 \\qquad \\textbf{(D) } 17 \\qquad \\textbf{(E) } 19$", "description_html": "<p>If the positive integer  <span class=\"katex--inline\">c</span>  has positive integer divisors  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  with  <span class=\"katex--inline\">c = ab</span> , then  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span>  are said to be  <span class=\"katex--inline\">\\textit{complementary}</span>  divisors of  <span class=\"katex--inline\">c</span> . Suppose that  <span class=\"katex--inline\">N</span>  is a positive integer that has one complementary pair of divisors that differ by  <span class=\"katex--inline\">20</span>  and another pair of complementary divisors that differ by  <span class=\"katex--inline\">23</span> . What is the sum of the digits of  <span class=\"katex--inline\">N</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 9 \\qquad \\textbf{(B) } 13\\qquad \\textbf{(C) } 15 \\qquad \\textbf{(D) } 17 \\qquad \\textbf{(E) } 19</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": 4, "problem_name": "2023 AMC 10A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10A_p24", "prev": "/problem/23_amc10A_p22"}}