2018 AMC 12A Problem 25

For a positive integer n and nonzero digits a, b, and c, let A_n be the n-digit integer each of whose digits is equal to a; let B_n be the n-digit integer each of whose digits is equal to b, and let C_n be the 2n-digit (not n-digit) integer each of whose digits is equal to c. What is the greatest possible value of a + b + c for which there are at least two values of n such that C_n - B_n = A_n^2?

\textbf{(A) } 12 \qquad \textbf{(B) } 14 \qquad \textbf{(C) } 16 \qquad \textbf{(D) } 18 \qquad \textbf{(E) } 20

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.