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4x^3 - 3x + 1 = 2y^2 has at least 31 solutions

Source: Donova MO 2005, problem 1

February 11, 2006
trigonometrynumber theory proposednumber theory

Problem Statement

Prove that the equation 4x3−3x+1=2y24x^3-3x+1=2y^2 has at least 3131 solutions in positive integers xx and yy with x≤2005x\leq 2005.
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