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2^{n+2}(2^n-1)-8.3^n+1 is a perfect square

Source: Vietnamese TST 2011 P5

April 27, 2011
inductionmodular arithmeticnumber theoryPerfect Squares

Problem Statement

Find all positive integers nn such that A=2n+2(2n−1)−8⋅3n+1A=2^{n+2}(2^n-1)-8\cdot 3^n +1 is a perfect square.
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