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x^3 + 2x + 1 = 2^n

Source: Serbian Mathematical Olympiad 2007

June 9, 2007
modular arithmeticinequalitiesquadraticsnumber theorygreatest common divisornumber theory proposed

Problem Statement

Determine all pairs of natural numbers (x;n)(x; n) that satisfy the equation x3+2x+1=2n.x^{3}+2x+1 = 2^{n}.
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