Primality & Factoring

Gerry · science forum beginner Joined: 11 Nov 2005 Posts: 23

Two questions relating the following function:

N(r,x,y,z)=r^2+(z^2y+(2z+1)x)r+z^2(z^2-1)y^2/4+z(z^2+(z-1)/2)yx+z(z+1)x^2

1) How can i determine solutions for variables r,x,y,z if N is given?

2) For which range of the variables r,x,y,z can N be prime?

Any comments are welcome.

Gerry · science forum beginner Joined: 11 Nov 2005 Posts: 23

For example
493=N(r,x,y,z)=N(5,4,4,2)=N(9,8,4,1)=N(11,6,6,1)=N(17,12,8,0)
( Variables r,x,y,z >0 and integer are of interest)

Dave Rusin · science forum Guru Joined: 25 Mar 2005 Posts: 487

In article <1153219509.405937.291020@i42g2000cwa.googlegroups.com>,
Gerry <GerryMrt@gmail.com> wrote:

Gerry · science forum beginner Joined: 11 Nov 2005 Posts: 23

1) Interesting approach.
Would it be possible to create a faster algorithm than normal factoring
by trying to fit p and q as follows:
N=pq, p=yz^2/2+(x-y/2)z+r , q=y(z+1)^2/2+(x-y/2)(z+1)+r

Gerry

Sorry about the wrong group.

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