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math.NT2018★ 1 cited
On an infinite number of solutions to the Diophantine equation over the square integer matrices
I. Kaddoura, B. Mourad
In this paper, we use some extension of the Cayley-Hamilton theorem to find a family of matrices with integer entries that satisfy the non-linear Diophantine equation $ x^{n}+y^{p}…
math.NT2017★ 1 cited
On a new closed formula for the solution of second order linear difference equations and applications
Issam Kaddoura, Bassam Mourad
In this note, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory. This, in…