Issam Kaddoura, Bassam Mourad
Abstract
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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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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.
Key concepts: Diophantine equation, Integer (computer science), Mathematics, Diophantine set, Extension (predicate logic), Combinatorics, Square number, Square (algebra)