Problem

Given c2 - c + 1 = 0. Calculate c5036 + 1/ c5036

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Solution

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Here is my solution:

c - 1+1/c = 0, so  c+1/c =1.

c3 +1 = (c+1)( c2 - c + 1) = 0.

c5036 = (c3)1678 c2 = c2

so c5036 + 1/ c5036 = c2 + 1/ c2 = (c+1/c)2 – 2 = -1.