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Factors of the form N^2 - 3N +1

  1. Jan 12, 2006 #1
    I noted the following relation for the form [tex] F_{n} = n^{2}-3n+1[/tex]
    let [tex]p_n[/tex] be any whole factor of [tex] F_n[/tex] and [tex]p_{n}^{'}[/tex] be the quotient. The following relation then holds

    [tex]\frac{F_{n}}{p} * \frac{F_{(n+p)}}{p} = F_{(n+p_{n}^{'})}

    A trivial example would be to let p = 1. Then
    [tex] F_{n} * F_{(n+1)} = F_{(n+F_{n})}

    Is this something that is of interest?
  2. jcsd
  3. Jan 12, 2006 #2

    matt grime

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    You could at least put closing /tex's in. It is common to let quotients be q's and i notice that the subscript n's vanish in your (non-closed off) latex, should they?
  4. Jan 12, 2006 #3


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    I think you're saying something equivalent to: f(n)=n^2-3*n+1, and if f(n)=a*b for some n, then f(n+a)/a=f(n+b)/b. This is actually true for any monic quadradic polynomial with integer coefficients.
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