# A report on Binary quadratic form

Quadratic homogeneous polynomial in two variables

- Binary quadratic form6 related topics with Alpha

## Bhargava cube

0 linksConfiguration consisting of eight integers placed at the eight corners of a cube.

Configuration consisting of eight integers placed at the eight corners of a cube.

To each pair of opposite faces of a Bhargava cube one can associate an integer binary quadratic form thus getting three binary quadratic forms corresponding to the three pairs of opposite faces of the Bhargava cube.

## Genus of a quadratic form

0 linksClassification of quadratic forms and lattices over the ring of integers.

Classification of quadratic forms and lattices over the ring of integers.

For binary quadratic forms there is a group structure on the set C of equivalence classes of forms with given discriminant.

## Fermat's theorem on sums of two squares

0 linksOdd prime p can be expressed as:

Odd prime p can be expressed as:

An (integral binary) quadratic form is an expression of the form, as required.

## Manjul Bhargava

0 linksCanadian-American mathematician.

Canadian-American mathematician.

His PhD thesis generalized Gauss's classical law for composition of binary quadratic forms to many other situations.

## Infrastructure (number theory)

0 linksInfrastructure is a group-like structure appearing in global fields.

Infrastructure is a group-like structure appearing in global fields.

D. Shanks observed the infrastructure in real quadratic number fields when he was looking at cycles of reduced binary quadratic forms.

## Ideal class group

0 linksAlgebraic number field

Algebraic number field

For d < 0, the ideal class group of Q(√d) is isomorphic to the class group of integral binary quadratic forms of discriminant equal to the discriminant of Q(√d).