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Math Problem Inquiry Involving nonzero polynomials

  1. May 14, 2004 #1
    Find a nonzero polynomial f(w, x, y, z) in the four indeterminates w, x, y, and z of minimum degree such that switching any two indeterminates in the polynomial gives the same polynomial except that its sign is reversed. For example, f(z, x, y,w) = -f(w, x, y, z). Prove that the degree of the polynomial is as small as possible.

    No clue how to approach/sove.
    Any advice/tips or solutions would be great!

  2. jcsd
  3. May 15, 2004 #2

    matt grime

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    Science Advisor
    Homework Helper

    the best tip as always is for you to write out some polynomials ans swap over the variables and see what happens and try and find a solution that way
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