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2023 AMC 10A Problem 23

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2023 AMC 10A Problem 23AMC 10 Step by Step

Name: Date: September 13, 2026

Diophantine Equations · difficulty 4 of 5 · about 6 min · position P21-25

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 $N$ ?

A)
$9$
B)
$13$
C)
$15$
D)
$17$
E)
$19$

2023 AMC 10A Problem 23

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