fundamental discriminant
In mathematics, a fundamental discriminant D is an integer invariant in the theory of integral binary quadratic forms. If Q(x, y) = ax2 + bxy + cy2 is a quadratic form with integer coefficients, then D = b2 − 4ac is the discriminant of Q(x, y). Conversely, every integer D with D ≡ 0, 1 (mod 4) is the discriminant of some binary quadratic form with integer coefficients. Thus, all such integers are referred to as discriminants in this theory. There are explicit congruence conditions that give the set of fundamental discriminants. Specifically, D is a fundamental discriminant if and only if one of the following statements holds D ≡ 1 (mod 4) and is square-free, D = 4m, where m ≡ 2 or 3 (mod 4) and m is square-free.The first ten positive fundamental discriminants are: 1, 5, 8, 12, 13, 17, 21, 24, 28, 29, 33 (sequence A003658 in the OEIS).The first ten negative fundamental discriminants are: −3, −4, −7, −8, −11, −15, −19, −20, −23, −24, −31 (sequence A003657 in the OEIS).
integer invariant of integral binary quadratic forms, associating the integer ²−4 to the quadratic form ²++²
invariant