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    Totient function proof

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    For n in Z, n>=2 let phi n denote Euler's totient function.....

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    Solution Preview

    (a) Recall that the field of complex numbers C has phi (n) primitive n-th roots of unity,
    hence the n-th cyclotomic polynomial PHI_n also has degree phi(n), where

    PHI_n (x) = Product_{e primitive} (x - e)

    (b) If C_n denotes the cyclic group of order n, then C_{mn} ~ C_m x C_n if and only if m and n
    are relatively (coprime). Also, C_n has phi(n) elements of order n.

    It is ...

    Solution Summary

    This provides an example of a set of proofs regarding Euler's totient function.