On some symmetries of the base $ n $ expansion of $ 1/m $ : Comments on Artin's Primitive root conjecture
Suppose $ m,n\geq 2 $ are co prime integers. We prove certain new symmetries of the base $ n $ representation of $ 1/m $, and in particular characterize the subgroup generated by $ n $ inside $ (\mathbb{Z}/m\mathbb{Z})^\times $. As an application we give a sufficient condition for a prime $ p $ such...
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| creator | Chakraborty, Kalyan Krishnamoorthy, Krishnarjun |
| description | Suppose $ m,n\geq 2 $ are co prime integers. We prove certain new symmetries
of the base $ n $ representation of $ 1/m $, and in particular characterize the
subgroup generated by $ n $ inside $ (\mathbb{Z}/m\mathbb{Z})^\times $. As an
application we give a sufficient condition for a prime $ p $ such that a non
square number $ n $ is a primitive root modulo $ p $. |
| doi_str_mv | 10.48550/arxiv.2107.12121 |
| format | Article |
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of the base $ n $ representation of $ 1/m $, and in particular characterize the
subgroup generated by $ n $ inside $ (\mathbb{Z}/m\mathbb{Z})^\times $. As an
application we give a sufficient condition for a prime $ p $ such that a non
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subgroup generated by $ n $ inside $ (\mathbb{Z}/m\mathbb{Z})^\times $. As an
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of the base $ n $ representation of $ 1/m $, and in particular characterize the
subgroup generated by $ n $ inside $ (\mathbb{Z}/m\mathbb{Z})^\times $. As an
application we give a sufficient condition for a prime $ p $ such that a non
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| subjects | Mathematics - Number Theory |
| title | On some symmetries of the base $ n $ expansion of $ 1/m $ : Comments on Artin's Primitive root conjecture |
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