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arXiv · 2108.03198

Integer circulant determinants of order 15

Bishnu Paudel·Chris Pinner
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Abstract

We consider the values taken by $n\times n$ circulant determinants with integer entries when $n$ is the product of two distinct odd primes $p,q$. These correspond to the integer group determinants for $\mathbb Z_{pq}$, the cyclic group of order $pq$. We show that $p^2$ and $q^2$ are not determinants (more generally we show that the classic necessary divisibility conditions are never sufficient when $n$ contains at least two odd primes). We obtain a complete description of the integer group determinants for $\mathbb Z_{15}$ (the smallest unresolved group) and partial results for general $n=3p.$

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Bishnu Paudel, Chris Pinner. 2021-08-06. Integer circulant determinants of order 15. https://arxiv.org/abs/2108.03198

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