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Polynomial classes?

  1. May 18, 2008 #1
    Here are two very similar questions about polynomials that I feel may have deeper roots (excuse pun).

    a) Does anyone know of any interesting theory related to them that I could read up upon?

    b) How would one start solving them?

    Here are the problems:

    1) Show that there are infinitely many polynomials p with integer coefficients such that P(x^2 - 1) = (P(x))^2 - 1, P(0) =0 .

    2) Are there real polynomials p satisfying P(x^2 - 1) = (P(x))^2 + 1 for all x? If so, determine what they look like.

    Observe the plus sign at the end of the second problem.
  2. jcsd
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