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Putnam 1986 B2

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August 5, 2019
Putnamcomplex numbers

Problem Statement

Prove that there are only a finite number of possibilities for the ordered triple T=(x−y,y−z,z−x)T=(x-y,y-z,z-x), where x,y,zx,y,z are complex numbers satisfying the simultaneous equations x(x−1)+2yz=y(y−1)+2zx=z(z−1)+2xy, x(x-1)+2yz = y(y-1)+2zx = z(z-1)+2xy, and list all such triples TT.
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