DefinitionDefinition: Literature-sourcedProof: Not applicableSession-authored (Fable 5 assisted)judge pass (gpt-5.6-terra)audited 2026-08-26

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Integral binary quadratic forms

An integral binary quadratic form is a homogeneous polynomial

$f (x, y) = a x^{2} + b x y + c y^{2}$

with coefficients $a, b, c \in Z$ . We also denote this form by the triple

$f = (a, b, c) .$

The coefficient of $x y$ is written as $b$ , not $2 b$ .

The variables are two independent integer variables, so "binary" refers to the number of variables and "quadratic" to the total degree.
Later items pass freely between the polynomial notation $a x^{2} + b x y + c y^{2}$ and the coefficient notation $(a, b, c)$ .

Used by

Nothing. This result depends on no other item in the library.