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Math Prize 2017 Problem 13

Source:

September 26, 2017
Math Prize for Girls

Problem Statement

A polynomial whose roots are all equal to each other is called a unicorn. Compute the number of distinct ordered triples (M,P,G)(M, P, G), where MM, PP, GG are complex numbers, such that the polynomials z3+Mz2+Pz+Gz^3 + M z^2 + Pz + G and z3+Gz2+Pz+Mz^3 + G z^2 + Pz + M are both unicorns.
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