@article{oai:tuis.repo.nii.ac.jp:00000543,
 author = {鈴木, 英男 and Suzuki, Hideo},
 issue = {1},
 journal = {東京情報大学研究論集},
 month = {Sep},
 note = {P(論文), The primitive roots in ${\mathbb Z}_n^\times$ are defined and exist iff $n = 2, 4, p^{\alpha}, 2p^{\alpha}$. Knuth gave the definition of the primitive roots in ${\mathbb Z}_{p^\alpha}^\times$, and showed the necessary and sufficient condition for testing a primitive root in ${\mathbb Z}_{p^\alpha}^\times$. In this paper we define the primitive elements in ${\mathbb Z}_n^\times$, which is a generalization of primitive roots, as elements that take the maximum multiplicative order.And we give two theorems for the reduced testing of a primitive element in ${\mathbb Z}_n^\times$ for any composite $n$. It is shown that the two theorems, using a technique of a lemma, for testing a primitive element allow us an effective reduction in testing processes and in computing time cost as a consequence., The primitive roots in ${\mathbb Z}_n^\times$ are defined and exist iff $n = 2, 4, p^{\alpha}, 2p^{\alpha}$. Knuth gave the definition of the primitive roots in ${\mathbb Z}_{p^\alpha}^\times$, and showed the necessary and sufficient condition for testing a primitive root in ${\mathbb Z}_{p^\alpha}^\times$. In this paper we define the primitive elements in ${\mathbb Z}_n^\times$, which is a generalization of primitive roots, as elements that take the maximum multiplicative order.And we give two theorems for the reduced testing of a primitive element in ${\mathbb Z}_n^\times$ for any composite $n$. It is shown that the two theorems, using a technique of a lemma, for testing a primitive element allow us an effective reduction in testing processes and in computing time cost as a consequence.},
 pages = {41--47},
 title = {On the Reduced Testing of a Primitive Element in ${\\mathbb Z}_n^\\times$},
 volume = {19},
 year = {2015},
 yomi = {スズキ, ヒデオ}
}