Abstract
Let n be any natural number such that 2 is a primitive root of \(2n+1\). In this article, we prove that the permutation (n!) has two orbits if and only if \(2n+1=p^2\) for some odd prime p, where \((n!)={\prod \limits _{k=0}^{n-1}(1,2,\dots ,(n-k))}\).
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References
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Ramesh, V. P., Thangadurai, R., Makeshwari, M. & Sinha, S. (2020). A necessary and sufficient condition for \(2\) to be a primitive root of \(2p+1\), Mathematics Student, Indian Mathematical Society, 89(3-4), 171-176.
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We thank the reviewers of JRMS and IJPAM for carefully going through this manuscript and also for various comments improving the presentation.
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Communicated by Sanoli Gun.
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Ramesh, V.P., Makeshwari, M. & Sinha, S. Connecting primitive roots and permutations. Indian J Pure Appl Math (2023). https://doi.org/10.1007/s13226-023-00384-4
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DOI: https://doi.org/10.1007/s13226-023-00384-4