On an infinite number of solutions to the Diophantine equation $ x^{n}+y^{p}=z^{q}$ over the square integer matrices

I. Kaddoura; B. Mourad

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arXiv · 1808.09956

On an infinite number of solutions to the Diophantine equation $ x^{n}+y^{p}=z^{q}$ over the square integer matrices

I. Kaddoura·B. Mourad

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Abstract

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}=z^{q}$ where $n,p$ and $q$ are arbitrary positive integers.

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I. Kaddoura, B. Mourad. 2018-08-29. On an infinite number of solutions to the Diophantine equation $ x^{n}+y^{p}=z^{q}$ over the square integer matrices. https://arxiv.org/abs/1808.09956

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