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    Theory of Numbers
    Mobius Theorem

    The Mobius Inversion Formula
    1) Prove that ∑ μ(d) φ(d) = Π (2 - p)
    d/n p/n
    Primitive roots modulo p
    2) Find all primitive roots modulo 5, modulo 9, modulo 11, modulo 13 and modulo 15.

    Prime Numbers
    3) The Fermat numbers are numbers of the form 2^(2^n) + 1 = φn .
    Prove that if n < m, then &#966;n| &#966;m - 2

    4) Prove that if n &#8800; m, then gcd (&#966;n, &#966;m) = 1

    5) Use the above exercise to give a proof that there exist infinitely many primes.

    See the attached file.

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    Theory of Numbers
    Mobius Theorem

    The ...

    Solution Summary

    This solution is comprised of a detailed explanation of the Mobius Inversion Formula,
    Primitive roots modulo p and Fermat numbers.
    It contains step-by-step explanation for the following problem:

    The Mobius Inversion Formula
    1) Prove that &#8721; &#956;(d) &#966;(d) = &#928; (2 - p)
    d/n p/n
    Primitive roots modulo p
    2) Find all primitive roots modulo 5, modulo 9, modulo 11, modulo 13 and modulo 15.

    Prime Numbers
    3) The Fermat numbers are numbers of the form 2^(2^n) + 1 = &#966;n .
    Prove that if n < m, then &#966;n| &#966;m - 2

    4) Prove that if n &#8800; m, then gcd (&#966;n, &#966;m) = 1

    5) Use the above exercise to give a proof that there exist infinitely many primes.

    Solution contains detailed step-by-step explanation.

    $2.49

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