| viXra.org > Number Theory > viXra:2409.0031 |
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| viXra.org > Number Theory > viXra:2409.0031 |
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Number Theory |
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Authors: Walter A. Kehowski
Given $n=p_1^{e_1}cdots p_k^{e_k}$, there is a canonical isomorphism $mathbb{Z}_ncongmathbb{Z}_{p_1^{e_1}} oplus cdots oplus mathbb{Z}_{p_k^{e_k}}$. The spectral basis of $mathbb{Z}_n$ is an explicit realization of this isomorphism within $mathbb{Z}_n$ itself. This paper is a study of those numbers whose spectral basis consists of primes and powers. For example, if $M_p$ is a Mersenne prime with exponent $p$, then $2M_p$ has spectral basis ${M_p,2^{p}}$, while $2^pM_p$ has spectral basis ${M_p^2,2^{p}}$. Isospectral and isotropic numbers are introduced and many other numbers with interesting spectral bases are presented.
Comments: 61 Pages.
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[v1] 2024-09-06 03:39:51
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