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All reals a,b,c,d s.t. a + bcd = b + cda = c + dab = d + abc

Source: Austrian Mathematical Olympiad 2004, Part 1, P1

June 18, 2011
algebra proposedalgebra

Problem Statement

Find all quadruples (a,b,c,d)(a, b, c, d) of real numbers such that a+bcd=b+cda=c+dab=d+abc.a + bcd = b + cda = c + dab = d + abc.
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