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Problem of the Week 1182

A Power Sum Puzzle

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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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8 June 2014