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Thread: Irrationality proof

  1. #1
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    Irrationality proof

    Prove that:

    If a,b are relatively prime integers, and b is not a power of 2, then

    \frac{1}{\pi}\arccos\left (\frac{a}{b}\right )

    is irrational.
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  2. #2
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    Re: Irrationality proof

    we need the following result
    for each natural number n\geq  2 there is a polynomial function of degree n with integer coefficients

    f(x)=2^{n-1}x^n+ a_{n-1}x^{n-1}+\text{...}+a_0

    such that

    \cos (n x)=f(\cos (x))
    Last edited by Idea; Dec 8th 2014 at 01:58 AM.
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  3. #3
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    Re: Irrationality proof

    Yes, this is the way I obtained this result
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