利用者:东方大学名誉教授/sandbox

この数式はただのメモ代わりです。

${\sqrt[{N}]{rm_{1}}}={\sqrt[{N}]{p_{1}^{N+s_{1}-s_{1}\,{\bmod {\ }}N}p_{2}^{N+s_{2}-s_{2}\,{\bmod {\ }}N}p_{3}^{N+s_{3}-s_{3}\,{\bmod {\ }}N}\cdots p_{k}^{N+s_{k}-s_{k}\,{\bmod {\ }}N}}}$

$=p_{1}^{\frac {N+s_{1}-s_{1}\,{\bmod {\ }}N}{N}}p_{2}^{\frac {N+s_{2}-s_{2}\,{\bmod {\ }}N}{N}}p_{3}^{\frac {N+s_{3}-s_{3}\,{\bmod {\ }}N}{N}}\cdots p_{k}^{\frac {N+s_{k}-s_{k}\,{\bmod {\ }}N}{N}}$

$n={\sqrt[{N}]{rm_{1}}}={\sqrt[{N}]{\prod _{i=1}^{k}p_{i}^{N+s_{i}-\left(s_{i}{\bmod {\ }}N\right)}}}$

$=\prod _{i=1}^{k}p_{i}^{\frac {N+s_{i}-\left(s_{i}{\bmod {\ }}N\right)}{N}}$

$n^{N}=(rq+s)^{N}=\sum _{m=0}^{N}\ _{N}C_{m}(rq)^{N-m}s^{m}$

$=r\left(\sum _{m=0}^{N-1}\ _{N}C_{m}r^{N-m-1}q^{N-m}s^{m}\right)+s^{N}$

$s_{min}^{N}=\left(\prod _{\alpha =1}^{k}p_{i\alpha }^{\left\lceil {\frac {t_{i\alpha }}{N}}\right\rceil N}\right)\left(\prod _{\alpha =1}^{k}p_{j\alpha }^{N}\right)$

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