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Powers of 3 and Floors

Source:

August 8, 2024
floor functionnumber theory2022

Problem Statement

Let ⌊x⌋\lfloor x \rfloor denote the greatest integer less than or equal to xx. Find the number of positive integers mm between 11 and 20222022 inclusive such that ⌊3m11⌋ \left\lfloor \frac{3^m}{11} \right\rfloor is even.
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