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JBMO 2010. Problem 1.

Source:

June 20, 2010
algebrapolynomialfunctionalgebra proposed

Problem Statement

The real numbers aa, bb, cc, dd satisfy simultaneously the equations abc−d=1,   bcd−a=2,   cda−b=3,   dab−c=−6.abc -d = 1, \ \ \ bcd - a = 2, \ \ \ cda- b = 3, \ \ \ dab - c = -6. Prove that a+b+c+d≠0a + b + c + d \not = 0.
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