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Results tagged with quadratic-forms
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user 38889
Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.
16
votes
What is known about primes of the form $x^2-2y^2$?
As $2 = x^2 -2y^2$ for $x = 2$ and $y=1$ we fix an odd prime number $p$, and
Claim: There exist integers $x,y$ such that $p = x^2 -2y^2$ if and only if $p \equiv \pm1 \mod 8$.
First if $p = x^2 -2y …
- 11.3k
19
votes
Accepted
What is known about primes of the form $x^2-2y^2$?
Take any square free $1 \neq n \in \mathbb{N}$ and recall that $R_n = \mathbb{Z}[\sqrt{n}]$ has a multiplicative norm function $N \colon R \to \mathbb{Z}$ given by $N(x + y\sqrt{n}) = x^2 -ny^2$ so a …
- 11.3k