IMO 1979 LL ROM55

Let a, b be coprime integers. Show that the equation ax2 +

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IMO 1979 LL ROM55

Origin: ROM

Problem

Let a, b be coprime integers. Show that the equation ax2 + by2 = z3 has an infinite set of solutions (x, y, z) with x, y, z \inZ and x, y mutually coprime (in each solution).