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Putnam 1956 B7

Source: Putnam 1956

July 5, 2022
Putnamalgebrapolynomialroots

Problem Statement

The polynomials P(z)P(z) and Q(z)Q(z) with complex coefficients have the same set of numbers for their zeros but possibly different multiplicities. The same is true for the polynomials P(z)+1    and    Q(z)+1.P(z)+1 \;\; \text{and} \;\; Q(z)+1. Prove that P(z)=Q(z).P(z)=Q(z).
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