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Thread: euler phi function

  1. #1
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    euler phi function

    Let n be within Z with n>0. Prove that the number of fractions a/b in lowest terms with 0<a/b1 and bn is
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  2. #2
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    The factions are:

    $\displaystyle x/1$, [1]
    $\displaystyle x/2$, [2]
    $\displaystyle x/3$, [3]
    ...
    $\displaystyle x/n$. [4]

    In [1] the number of reduced fractions is $\displaystyle \phi (1)$.
    In [2] the number of reduced fractions is $\displaystyle \phi (2)$.
    In [3] the number of reduced fractions is $\displaystyle \phi(3)$.
    ...
    In [4] the number of reduced fractions is $\displaystyle \phi(n)$.

    Thus, in total we have $\displaystyle \phi ( 1) + ... + \phi(n)$ such fractions.
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