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On the matrix negative Pell equation

100%

Grytczuk A., Kurzydło I.

Discussiones Mathematicae - General Algebra and Applications

2009

tom 29

nr 1

35-45

Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) $∑_{i=1}^{n} X₂_{i} - d ∑_{i=1}^{n} Y²_{i} = -I$ with d ∈ N for nonsingular $X_{i},Y_{i} ∈ M₂(Z)$, i=1,...,n.

Some classes of Diophantine equations connected with McFarland's and Ma's conjectures

100%

Cao Z., Grytczuk A.

Discussiones Mathematicae - General Algebra and Applications

2000

tom 20

nr 2

193-198

In this paper we consider some special classes of Diophantine equations connected with McFarland's and Ma's conjectures about difference sets in abelian groups and we obtain an extension of known results.

Ograniczanie wyników

2 Discussiones Mathematicae - General Algebra and Applications

2 Grytczuk A.

1 Cao Z.

1 Kurzydło I.

1 2009

1 2000

Wyniki wyszukiwania

On the matrix negative Pell equation

Some classes of Diophantine equations connected with McFarland's and Ma's conjectures