On Divisibility of the Class Number of a Real Abelian Field and Fermat Quotients

Key Points

• This research aims to establish improved conditions for the divisibility of class numbers in real abelian fields based on Fermat quotients.
• Building upon previous work by Jakubec and Metsnkyl
• Employing different mathematical techniques to refine existing conditions
• Defines new sufficient conditions for r h K, where r is an odd prime and h K is the class number of K.
• Clarifies relationships between the class number and Fermat quotients associated with cyclotomic elements.