Difference between revisions of "2018 AMC 12A Problems/Problem 25"

Latest revision as of 14:41, 8 February 2018

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-===Problem===
+#REDIRECT[[2018_AMC_10A_Problems/Problem_25]]
-For a positive integer <math>n</math> and nonzero digits <math>a</math>, <math>b</math>, and <math>c</math>, let <math>A_n</math> be the <math>n</math>-digit integer each of whose digits is equal to <math>a</math>; let <math>B_n</math> be the <math>n</math>-digit integer each of whose digits is equal to <math>b</math>; and let <math>C_n</math> be the <math>2n</math>-digit (not <math>n</math>-digit) integer each of whose digits is equal to <math>c</math>. What is the greatest possible value of <math>a+b+c</math> for which there are at least two values of <math>n</math> such that <math>C_n - B_n = A_n^2</math>?
-<math> \textbf{(A)}\ 12 \qquad\textbf{(B)}\ 14\qquad\textbf{(C)}\ 16\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 20 </math>