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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.