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Math Help - Relatively prime / Quadratic forms

  1. #1
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    Relatively prime / Quadratic forms

    This is really simple.

    A quadratic form ax^2+bxy+cy^2 is called "primitive" if a,b,c are relatively prime.

    A primitive positive definite form is said to be reduced if:

    |b| <= a <= c and b=>0 if either |b|=a or a=c. (where "<=" indicates a non-strict inequality).

    So how can a,b,c be relatively prime, and then we say |b|=a or a=c?
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  2. #2
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    Quote Originally Posted by brisbane View Post
    This is really simple.

    A quadratic form ax^2+bxy+cy^2 is called "primitive" if a,b,c are relatively prime.

    A primitive positive definite form is said to be reduced if:

    |b| <= a <= c and b=>0 if either |b|=a or a=c. (where "<=" indicates a non-strict inequality).

    So how can a,b,c be relatively prime, and then we say |b|=a or a=c?

    Where did you get this definition from? What does it mean that "a,b,c" are rel. prime? Pairwise or (a,b,c)=1? If pairwise then it obviously cannot be |b|=a or a=c, so it must be the other option...
    Is this from some book? Which one?

    Tonio
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