Class Number One Problem for a Non-richaud-Degert Type Family of Real Quadratic Fields

Nimish Kumar  Mahapatra

doi:10.5644/SJM.19.01.09

Class Number One Problem for a Non-richaud-Degert Type Family of Real Quadratic Fields

Authors

Nimish Kumar Mahapatra Indian Institute of Science Education and Research Berhampur Department of Mathematical Sciences Transit campus (Govt. ITI Building) Engg. School Junction Berhampur

DOI:

https://doi.org/10.5644/SJM.19.01.09

Keywords:

Real quadratic ﬁeld, Class number, Diophantine equation

Abstract

We study the class number one problem for a one parameter family of real quadratic fields $\mathbb{Q}(\sqrt{d})$, where $d=100m^2+ 28m+2$ and $m$ is a positive integer. We show that there is no such field with class number one.

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Published

17.01.2024

How to Cite

Mahapatra, N. K. . (2024). Class Number One Problem for a Non-richaud-Degert Type Family of Real Quadratic Fields. Sarajevo Journal of Mathematics, 19(1), 105–108. https://doi.org/10.5644/SJM.19.01.09