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Thread: Factoring with Complex Numbers using Trig

  1. #1
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    Factoring with Complex Numbers using Trig

    I need help with a problem I'm trying to solve:

    In terms of n, what is the highest degree polynomial obtained when factoring xn-yn over the reals.

    I have found the answer to be φ(n), but am unable to prove it. Can anybody help?
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  2. #2
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    Re: Factoring with Complex Numbers using Trig

    Quote Originally Posted by jojothebobot View Post
    I need help with a problem I'm trying to solve:In terms of n, what is the highest degree polynomial obtained when factoring xn-yn over the reals.
    I have found the answer to be φ(n), but am unable to prove it. Can anybody help?
    Can you explain what "the highest degree polynomial obtained when factoring xn-yn over the reals" means?
    A polynomial is a one variable expression. But you have x & y.
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  3. #3
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    Re: Factoring with Complex Numbers using Trig

    Quote Originally Posted by Plato View Post
    A polynomial is a one variable expression. But you have x & y.
    Hmm, Wikipedia, MathWorld, PlanetMath and Springer Encyclopedia of Mathematics disagree.
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    Re: Factoring with Complex Numbers using Trig

    Quote Originally Posted by emakarov View Post
    Well there is no universal agreement in mathematical notation on anything.
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  5. #5
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    Re: Factoring with Complex Numbers using Trig

    Well, I too would be surprized to hear that x^2+ y^2 is not a polynomial.
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