Poulet Numbers which are also Magic Constant for Magic Square
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Theorem
The sequence of Poulet numbers which are also the magic constant of a magic square begins:
- $1105, 2465, \ldots$
Proof
From the sequence of Poulet numbers, these are Poulet numbers:
- $1105, 2465, \ldots$
Then we have:
\(\ds 1105\) | \(=\) | \(\ds \dfrac {13 \paren {13^2 + 1} } 2\) | so $1105$ is the magic constant of the order $13$ magic square | |||||||||||
\(\ds 2465\) | \(=\) | \(\ds \dfrac {17 \paren {17^2 + 1} } 2\) | so $2465$ is the magic constant of the order $17$ magic square |
This article is complete as far as it goes, but it could do with expansion. In particular: Further investigation needed. I have not seen this correspondence explored on the internet. I note though that both $1105$ and $2465$ are also Carmichael. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding this information. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Expand}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |