JP Journal of Algebra, Number Theory and Applications
Volume 62, Issue 2, Pages 159 - 165
(November 2023) http://dx.doi.org/10.17654/0972555523027 |
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NOTE ON THE CLASS NUMBER OF IMAGINARY QUADRATIC NUMBER FIELDS AND SOPHIE GERMAIN PRIMES
Anly Li
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Abstract: Let p > 2 be a Sophie Germain prime which means that q = 2p+1 is also a prime. Let and denote its ideal class number by hK. We use Kummer congruences and Bernoulli numbers to study the relation between p and We prove that for some positive integer k.
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Keywords and phrases: class number, Sophie Germain prime.
Received: August 29, 2023; Accepted: October 7, 2023; Published: November 6, 2023
How to cite this article: Anly Li, Note on the class number of imaginary quadratic number fields and Sophie Germain primes, JP Journal of Algebra, Number Theory and Applications 62(2) (2023), 159-165. http://dx.doi.org/10.17654/0972555523027
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] Kenneth F. Ireland and Michael I. Rosen, A Classical Introduction to Modern Number Theory, Springer, 1990. [2] Paulo Ribenboim, 13 Lectures on Fermat’s Last Theorem, Springer-Verlag, New York, 1979. [3] Tom Lovering, Cyclotomic fields and Fermat’s last theorem. https://tlovering.files.wordpress.com/2015/02/cyclotomic-fields-and-flt9.pdf.
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