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n power of 2 iff exists m so that 2^n-1 divides m^2 +9

Source: Czech and Slovak Match 2000 P3

October 1, 2017
number theorydivisorpower of 2

Problem Statement

Let nn be a positive integer. Prove that nn is a power of two if and only if there exists an integer mm such that 2nāˆ’12^n-1 is a divisor of m2+9m^2 +9.
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