Problem of the Week 1182

A Power Sum Puzzle

Suppose a, b, c, d are complex numbers such that

a  +  b  +  c  +  d  = 1
a² + b² + c² + d² = 0
a³ + b³ + c³ + d³ = 1
a⁴ + b⁴ + c⁴ + d⁴ = 0

What is a¹⁰ + b¹⁰ + c¹⁰ + d¹⁰?

Source: Due to Michael Elgersma and Stan Wagon, extending an old chestnut involving three variables and 3, 5, 7 on the right side.

© Copyright 2014 Stan Wagon. Reproduced with permission.

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