Binary quadratic form: Difference between revisions

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where ''a'', ''b'', ''c'' are the '''coefficients'''. When the coefficients can be arbitrary [[complex number]]s, most results are not specific to the case of two variables, so they are described in [[quadratic form]]. A quadratic form with [[integer]] coefficients is called an '''integral binary quadratic form''', often abbreviated to ''binary quadratic form''.

This article is entirely devoted to integral binary quadratic forms. This choice is motivated by their status as the driving force behind the development of [[algebraic number theory]]. Since the late nineteenth century, theybinary quadratic forms have beengiven mostlyup supplantedtheir preeminence in newalgebraic number developmentstheory byto [[quadratic field|quadratic]] and more general [[number field]]s, but advances specific to binary quadratic forms still occur on occasion.