{"created":"2023-05-15T12:16:58.395433+00:00","id":543,"links":{},"metadata":{"_buckets":{"deposit":"9fe32266-a3c0-4456-a1bc-d135ded4ef6a"},"_deposit":{"created_by":3,"id":"543","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"543"},"status":"published"},"_oai":{"id":"oai:tuis.repo.nii.ac.jp:00000543","sets":["1:4:157:158"]},"author_link":["2411","2412","2413"],"control_number":"543","item_1701328008552":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"東京情報大学","subitem_publisher_language":"ja"}]},"item_1_biblio_info_14":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2015-09-30","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"1","bibliographicPageEnd":"47","bibliographicPageStart":"41","bibliographicVolumeNumber":"19","bibliographic_titles":[{"bibliographic_title":"東京情報大学研究論集","bibliographic_titleLang":"ja"}]}]},"item_1_creator_6":{"attribute_name":"著者名(日)","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"鈴木, 英男","creatorNameLang":"ja"},{"creatorName":"スズキ, ヒデオ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Suzuki, Hideo","creatorNameLang":"en"}]}]},"item_1_creator_7":{"attribute_name":"著者名よみ","attribute_type":"creator","attribute_value_mlt":[{"nameIdentifiers":[{}]}]},"item_1_creator_8":{"attribute_name":"著者名(英)","attribute_type":"creator","attribute_value_mlt":[{"nameIdentifiers":[{}]}]},"item_1_description_1":{"attribute_name":"ページ属性","attribute_value_mlt":[{"subitem_description":"P(論文)","subitem_description_type":"Other"}]},"item_1_description_11":{"attribute_name":"抄録(日)","attribute_value_mlt":[{"subitem_description":"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.","subitem_description_type":"Other"}]},"item_1_description_12":{"attribute_name":"抄録(英)","attribute_value_mlt":[{"subitem_description":"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.","subitem_description_language":"en","subitem_description_type":"Other"}]},"item_1_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.15029/00000534","subitem_identifier_reg_type":"JaLC"}]},"item_1_source_id_13":{"attribute_name":"雑誌書誌ID","attribute_value_mlt":[{"subitem_source_identifier":"AA11155514","subitem_source_identifier_type":"NCID"}]},"item_1_text_10":{"attribute_name":"著者所属(英)","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"Tokyo University of Information Sciences, Faculty of Informatics"}]},"item_1_text_9":{"attribute_name":"著者所属(日)","attribute_value_mlt":[{"subitem_text_language":"ja","subitem_text_value":"東京情報大学総合情報学部"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2015-09-30"}],"displaytype":"detail","filename":"KJ00009952199.pdf","filesize":[{"value":"1.4 MB"}],"format":"application/pdf","license_note":"TUIS","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KJ00009952199","url":"https://tuis.repo.nii.ac.jp/record/543/files/KJ00009952199.pdf"},"version_id":"eb24bb44-02ed-41fa-9f71-7045eda0e78e"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"primitive element modulo a composite","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"primitive root","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"universal exponent","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"On the Reduced Testing of a Primitive Element in ${\\\\mathbb Z}_n^\\\\times$","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"On the Reduced Testing of a Primitive Element in ${\\\\mathbb Z}_n^\\\\times$","subitem_title_language":"en"},{"subitem_title":"On the Reduced Testing of a Primitive Element in ${\\\\mathbb Z}_n^\\\\times$","subitem_title_language":"ja"}]},"item_type_id":"1","owner":"3","path":["158"],"pubdate":{"attribute_name":"PubDate","attribute_value":"2015-09-30"},"publish_date":"2015-09-30","publish_status":"0","recid":"543","relation_version_is_last":true,"title":["On the Reduced Testing of a Primitive Element in ${\\\\mathbb Z}_n^\\\\times$"],"weko_creator_id":"3","weko_shared_id":-1},"updated":"2023-12-21T06:36:12.318873+00:00"}