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Problems(1)

China Mathematical Olympiad 1987 problem1

Source: China Mathematical Olympiad 1987 problem1

1/6/2014

Let

n

be a natural number. Prove that a necessary and sufficient condition for the equation

z^{n+1}-z^n-1=0

to have a complex root whose modulus is equal to

1

is that

n+2

is divisible by

6

trigonometryalgebra unsolvedalgebra