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

  • Thread starter ramsey2879
  • Start date
  • #1
841
0
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?
 

Answers and Replies

  • #2
matt grime
Science Advisor
Homework Helper
9,420
4
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?
 
  • #3
shmoe
Science Advisor
Homework Helper
1,992
1
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.
 

Related Threads on Factors of the form N^2 - 3N +1

Replies
4
Views
10K
Replies
3
Views
4K
Replies
7
Views
3K
Replies
9
Views
3K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
18
Views
4K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
7
Views
4K
Top