IMO 1988 LL USS86

Let a, b, c be integers different from zero. It is known that the

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IMO 1988 LL USS86

Origin: USS

Problem

Let a, b, c be integers different from zero. It is known that the equation ax2 + by2 + cz2 = 0 has a solution (x, y, z) in integers different from the solution x = y = z = 0. Prove that the equation ax2+by2+cz2 = 1 has a solution in rational numbers.