How Do Factors Relate in the Quadratic Form N^2 - 3N + 1?

[ramsey2879]

I noted the following relation for the form $$F_{n} = n^{2}-3n+1$$
let $$p_n$$ be any whole factor of $$F_n$$ and $$p_{n}^{'}$$ be the quotient. The following relation then holds

[tex]\frac{F_{n}}{p} * \frac{F_{(n+p)}}{p} = F_{(n+p_{n}^{'})}<br /> <br /> A trivial example would be to let p = 1. Then<br /> $$F_{n} * F_{(n+1)} = F_{(n+F_{n})} <br /> <br /> Is this something that is of interest?$$[/tex]

 

[matt grime]

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?

 

[shmoe]

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.