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Source: 2023 AIME II Problem #13

February 16, 2023
AIMEAIME II

Problem Statement

Let AA be an acute angle such that tan⁡A=2cos⁡A\tan A = 2\cos A. Find the number of positive integers nn less than or equal to 10001000 such that sec⁡nA+tan⁡nA\sec^n A + \tan^n A is a positive integer whose units digit is 99.
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