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Primitive binary quadratic forms
Definition
An integral binary quadratic form (Integral binary quadratic forms) is primitive when the only integers dividing all three coefficients , , and are and .
Equivalently, is primitive when there is no positive integer greater than dividing all three coefficients simultaneously.
Remarks
- Primitive forms and primitive representations are different notions: Integers represented, and primitively represented, by a binary quadratic form concerns the pair , whereas this definition concerns the coefficient triple .
- The word "primitive" here is invariant under changing all three coefficients by a common sign.
Depends on
Used by
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Sources
- William Stein, Elementary Number Theory and Elliptic Curves, Definition 9.4.2 (standard reference, not scraped)
- Andrew Granville, Binary Quadratic Forms, Chapter 4 (standard reference, not scraped)