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arXiv · 2110.12643

A diophantine problem concerning third order matrices

Ajai Choudhry
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Abstract

In this paper we find a third order unimodular matrix, none of whose entries is $1$ or $-1$, such that when each entry of the matrix is replaced by its cube, the resulting matrix is also unimodular. Further, we find third order square integer matrices $(a_{ij})$, none of the integers $a_{ij}$ being $1$ or $-1$, such that $\det{(a_{ij})}=k$ and $\det{(a_{ij}^3)}=k^3$, where $k$ is a nonzero integer.

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Ajai Choudhry. 2021-10-25. A diophantine problem concerning third order matrices. https://arxiv.org/abs/2110.12643

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