20040427, 05:10  #1 
11×811 Posts 
number theory help
a homogeneous polynomial in 2 variables x,y, of degree 2, say, f(x,y)=ax^2+bxy+cy^2 with a,b,c, all integers is called a quadratic form over the integers. the discriminant of the above quadratic form is d=b^24ac. a change of variables u,v, is x=αu+βv, y=λu+δv, α, β, λ, δ are all integers, αδβλ= Β±1. thus you get g(u,v)=f(x,y)=f(αu+βv, λu+δv).
>show that if f(x,y) is a quadratic form with positive discriminant, then the equation f(x,y)=n may have infinitely many solutions by exhibiting an example. thanks. 
20040502, 14:29  #2  
Mar 2004
29 Posts 
Quote:


20040502, 18:09  #3  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{3}×11^{3} Posts 
Quote:
An elliptic curve, E(x,y) is a polynomial which is cubic in x and quadratic in y. The formula given is indeed a quadratic form. The way in which it is phrased makes me almost certain that the original post was an attempt to get assistance with a homework problem. Paul Last fiddled with by xilman on 20040502 at 18:12 

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