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Czech-Polish-Slovak Match 2016

Source: Czech-Polish-Slovak Match 2016,P1,day 2

July 12, 2016
algebra

Problem Statement

Find all quadruplets (a,b,c,d)(a, b, c, d) of real numbers satisfying the system (a+b)(a2+b2)=(c+d)(c2+d2)(a + b)(a^2 + b^2) = (c + d)(c^2 + d^2) (a+c)(a2+c2)=(b+d)(b2+d2)(a + c)(a^2 + c^2) = (b + d)(b^2 + d^2) (a+d)(a2+d2)=(b+c)(b2+c2)(a + d)(a^2 + d^2) = (b + c)(b^2 + c^2) (Slovakia)
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