Paul Bilokon

Determinantal Diophantine Linear Algebra: Foundations and Lorentz--Fermat Factorization

We propose \emph{determinantal Diophantine linear algebra} as a systematic framework for integer and rational solutions of prescribed-determinant equations inside affine linear families of matrices. A datum consists of an integral affine matrix pencil\[ \mathcal A(\mathbf x)=A_0+...

Determinantal Diophantine Linear Algebra: Foundations and Lorentz--Fermat Factorization

We propose \emph{determinantal Diophantine linear algebra} as a systematic framework for integer and rational solutions of prescribed-determinant equations inside affine linear families of matrices. A datum consists of an integral affine matrix pencil\[ \mathcal A(\mathbf x)=A_0+...