IMO 1992 LL IRE34

Let a, b, c be integers. Prove that there are integers p1, q1, r1,

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IMO 1992 LL IRE34

Origin: IRE

Problem

Let a, b, c be integers. Prove that there are integers p1, q1, r1, p2, q2, r2 such that a = q1r2 −q2r1, b = r1p2 −r2p1, c = p1q2 −p2q1.