If I took a Chebyshev polynomial, is it possible to divide it completely by something that isn't a chebyshev polynomial?
edit - the question was answered but people were not sure about what I was asking. I would delete it but I think it's a good thing to know.
Is it possible to divide a Chebyshev Polynomial by an arbitrary polynomial that is not related to Chebyshev Polynomials?
After using triple, quadruple, and quintuple sequences on my maple program it seems the only thing that can divide into Chebyshev Polynomials are other Chebyshev Polynomials and polynomials that have solutions of Chebyshev Polynomials. But as it stands, something like x^2-x-1 (phi) can't divide into them. The reason I asked this is because the zeros of these polynomials have arclengths divisible by pi. If I were to divide the arclength of phi by pi, I would get a transcendental value. I think it's very interesting that these polynomials can't be divided by something that isn't related to them.