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2011•Honam Mathematical JournalOpen access

SEMI-PRIMITIVE ROOT MODULO n

Ki‐Suk Lee, Mi-Yeon Kwon, Min-Kyung Kang, Gi-Cheol Shin

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Abstract

Consider a multiplicative group of integers modulo n, denoted by $\mathbb{Z}_n^*$ . Any element $a{\in}\mathbb{Z}_n^*$ n is said to be a semi-primitive root if the order of a modulo n is $\phi$ (n)/2, where $\phi$ (n) is the Euler phi-function. In this paper, we classify the multiplicative groups of integers having semi-primitive roots and give interesting properties of such groups.

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Consider a multiplicative group of integers modulo n, denoted by $\mathbb{Z}_n^*$ . Any element $a{\in}\mathbb{Z}_n^*$ n is said to be a semi-primitive root if the order of a modulo n is $\phi$ (n)/2, where $\phi$ (n) is the Euler phi-function. In this paper, we classify the multiplicative groups of integers having semi-primitive roots and give interesting properties of such groups.

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Available abstract

Consider a multiplicative group of integers modulo n, denoted by $\mathbb{Z}_n^*$ . Any element $a{\in}\mathbb{Z}_n^*$ n is said to be a semi-primitive root if the order of a modulo n is $\phi$ (n)/2, where $\phi$ (n) is the Euler phi-function. In this paper, we classify the multiplicative groups of integers having semi-primitive roots and give interesting properties of such groups.

Key concepts: Primitive root modulo n, Modulo, Multiplicative function, Mathematics, Multiplicative group, Combinatorics, Root (linguistics), Order (exchange)

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