1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Polynomial proof help

  1. Sep 19, 2005 #1
    "Prove that


    can be written as a polynomial in [tex]n[/tex] of degree at most [tex]k+1[/tex]."

    Isn't this kinda trivial? I mean I know the "book" solution is to prove by induction, etc, but assuming that I have the above expression, I can prove or disprove it, depending on how I interpret the question.

    If it means that it can be written in the above conditions AND NOTHING ELSE, I can easily produce a counterexample:

    [tex]1+2+3 = 3^3 - 7\times3[/tex]

    If it means that it can be written in the above conditions, but does not prohibit the existence of other solutions, then it's trivial, because the above expression can be written as

    [tex]an^{k+1}[/tex] for some real number [tex]a[/tex]
  2. jcsd
  3. Sep 19, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    It doesn't mean "and nothing else", it's already written in a form that you wouldn't call a polynomial.

    No choice of a here will hold for all n. Your polynomial is supposed to equal that expression for all values of n.
  4. Sep 20, 2005 #3
    True, no choice of a will hold for every n, but there exists one for every n.
  5. Sep 20, 2005 #4


    User Avatar
    Science Advisor
    Homework Helper

    It's not a polynomial if the coefficients aren't constant. Your a will depend on n in some unspecified way, and you haven't solved the problem.
  6. Sep 20, 2005 #5
    No easy way out then. Damn.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Polynomial proof help
  1. Help polynomial (Replies: 5)

  2. Polynomial math help (Replies: 4)

  3. Polynomial Help (Replies: 4)

  4. Help with proofs (Replies: 2)

  5. Help with this proof (Replies: 1)