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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.02528 |
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| _version_ | 1866910030641496064 |
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| author | Cichacz, Sylwia Froncek, Dalibor |
| author_facet | Cichacz, Sylwia Froncek, Dalibor |
| contents | Let $(Γ,+)$ be an Abelian group of order $n^2$ and MS$_Γ(n)$ be an $n\times n$ array whose entries are all elements of $Γ$. Then MS$_Γ(n)$ is a $Γ$-magic square if all row, column, main and backward main diagonal sums are equal to the same element $μ\inΓ$. We prove that for every Abelian group $Γ$ of order $n^2$, $n>2$, there exists a magic square MS$_Γ(n)$ where the square entries are elements of $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Magic squares on Abelian groups Cichacz, Sylwia Froncek, Dalibor Combinatorics 05B15 Let $(Γ,+)$ be an Abelian group of order $n^2$ and MS$_Γ(n)$ be an $n\times n$ array whose entries are all elements of $Γ$. Then MS$_Γ(n)$ is a $Γ$-magic square if all row, column, main and backward main diagonal sums are equal to the same element $μ\inΓ$. We prove that for every Abelian group $Γ$ of order $n^2$, $n>2$, there exists a magic square MS$_Γ(n)$ where the square entries are elements of $Γ$. |
| title | Magic squares on Abelian groups |
| topic | Combinatorics 05B15 |
| url | https://arxiv.org/abs/2505.02528 |