number of biquadratic polynomials, f(n,m)=an²+bnm+cm²
 

A pleasant night for everyone,


i have 30 different polynomials with negativ discriminant and
256 different polynomials with positiv discriminant

of the form f(n)=n²+bn+c


( complete list under [url]http://devalco.de/poly_sec.php[/url] )


how many possibilities exist for the biquadratic forms f(n,m)=an²+bnm+cm²


I found the list of OEIS

[url]https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS[/url]


but i do not understand the relationship:
Can i combine every two polynomials

of the form f(n), f(m) into the form f(n,m) ?


Would be nice if you give me a hint.


Greetings from x²+Ny² :loco::hello::cmd::beatdown:

(the book Primes of the form x²+ny² from David A. Cox is very interesting)

Bernhard

[url]http://mathworld.wolfram.com/BiquadraticEquation.html[/url]

gcd(m,n)=1
gcd(a,b,c)=1
gcd(c,n)=1
gcd(a,m)=1

just for a start to not not have a non-trivial factor.