Originally Posted by math
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= ±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.
