このエントリーをはてなブックマークに追加
ID 56015
フルテキストURL
著者
Shimizu, Kenichi
抄録
We study a class of integers called SP numbers (Sum Prime numbers). An SP number is by de nition a positive integer d that gives rise to a prime number (a + b)=gcd(4; 1 + d) from every factorization d = ab. We also discuss properties of SP numbers in relations with arithmetic of imaginary quadratic elds (least split primes, exponents of ideal class groups). Further we point out that special cases of SP numbers provide the problems of distribution of prime numbers (twin primes, Sophi-Germain primes, quadratic progressions). Finally, we consider the problem whether there exist in nitely many SP numbers.
キーワード
SP number
prime number
imaginary quadratic fi eld
備考
Mathematics Subject Classi cation. Primary 11A41;Secondary 11R11,11R29
発行日
2018-01
出版物タイトル
Mathematical Journal of Okayama University
60巻
1号
出版者
Department of Mathematics, Faculty of Science, Okayama University
開始ページ
155
終了ページ
164
ISSN
0030-1566
NCID
AA00723502
資料タイプ
学術雑誌論文
オフィシャル URL
http://www.math.okayama-u.ac.jp/mjou/
言語
English
著作権者
Copyright©2018 by the Editorial Board of Mathematical Journal of Okayama University
論文のバージョン
publisher
査読
有り
Submission Path
mjou/vol59/iss1/8