Ljunggren's Diophantine problem connected with virus structure.
On the matrix negative Pell equation
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) with d ∈ N for nonsingular , i=1,...,n.
Some classes of Diophantine equations connected with McFarland's and Ma's conjectures
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.
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