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greatest power of 2 that divides a_n = [(3+\sqrt{11} )^{2n+1}]

Source: Austrian Polish 1979 APMC

April 26, 2020
floor functionpower of 2number theory

Problem Statement

Find the greatest power of 22 that divides an=[(3+11)2n+1]a_n = [(3+\sqrt{11} )^{2n+1}], where nn is a given positive integer.
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