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Equation has always a solution

Source: Finnish Mathematics Competition 1999, Final Round, Problem 1

November 14, 2011
calculusintegrationmodular arithmeticnumber theory unsolvednumber theory

Problem Statement

Show that the equation x3+2y2+4z=nx^3 + 2y^2 + 4z = n has an integral solution (x,y,z)(x, y, z) for all integers n.n.
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