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Math Help - Polynomial rings

  1. #1
    Junior Member
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    May 2008
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    70

    Polynomial rings

    Show that x^n = (a_i) where a_i = { 1 if i = n, 0 if otherwise| for all n >= 0}
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  2. #2
    Junior Member
    Joined
    May 2008
    Posts
    70

    Progress thus far

    So now I have:

    x = (ai) where ai = { 1 if i = 1, 0 if i <> 1

    x(bi) = (ai)(bi) = (di)
    where di = sum from j=0 to i of aj(bi-j) = a1(bi-1) = 1(bi-1) = bi-1, since aj=0 if j<>1

    but I don't know where to go from here..
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