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Effective results for Diophantine equations over finitely generated domains

Attila Bérczes, Jan-Hendrik Evertse, Kálmán Győry (2014)

Acta Arithmetica

Let A be an arbitrary integral domain of characteristic 0 that is finitely generated over ℤ. We consider Thue equations F(x,y) = δ in x,y ∈ A, where F is a binary form with coefficients from A, and δ is a non-zero element from A, and hyper- and superelliptic equations f ( x ) = δ y m in x,y ∈ A, where f ∈ A[X], δ ∈ A∖0 and m 2 . Under the necessary finiteness conditions we give effective upper bounds for the sizes of the solutions of the equations in terms of appropriate representations for A, δ, F, f, m. These...

Fermat's Equation in Matrices

Khazanov, Alex (1995)

Serdica Mathematical Journal

The Fermat equation is solved in integral two by two matrices of determinant one as well as in finite order integral three by three matrices.

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