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Prove that p_1, q_1, r_1, p_2, q_2, r_2 exist

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September 2, 2010
linear algebranumber theorysystem of equationsAdditive Number TheoryIMO ShortlistIMO Longlist

Problem Statement

Let a,b,ca, b, c be integers. Prove that there are integers p1,q1,r1,p2,q2,r2p_1, q_1, r_1, p_2, q_2, r_2 such that a=q1r2−q2r1,b=r1p2−r2p1,c=p1q2−p2q1.a = q_1r_2 - q_2r_1, b = r_1p_2 - r_2p_1, c = p_1q_2 - p_2q_1.
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