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

\frac{F_{n}}{p} * \frac{F_{(n+p)}}{p} = F_{(n+p_{n}^{&#039;})}<br /> <br /> A trivial example would be to let p = 1. Then<br /> F_{n} * F_{(n+1)} = F_{(n+F_{n})} &lt;br /&gt; &lt;br /&gt; Is this something that is of interest?

 

[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.