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Putnam 2020 B5

Source: 81st William Lowell Putnam Competition

February 22, 2021
PutnamPutnam 2020

Problem Statement

For j∈{1,2,3,4}j \in \{ 1,2,3,4\}, let zjz_j be a complex number with ∣zj∣=1| z_j | = 1 and zj≠1z_j \neq 1. Prove that 3−z1−z2−z3−z4+z1z2z3z4≠0.3 - z_1 - z_2 - z_3 - z_4 + z_1z_2z_3z_4 \neq 0.
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