Pell-type equations and class number of the maximal real subfield of a cyclotomic field
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We investigate the solvability of the Diophantine equation \(x^2-my^2=\pm p\) in integers for certain integer m and prime p. Then we apply these results to produce family of maximal real subfield of a cyclotomic field whose class number is strictly larger than 1.
KeywordsDiophantine equation Real quadratic fields Maximal real subfield of cyclotomic field Class number
Mathematics Subject ClassificationPrimary: 11D09 11R29 Secondary: 11R11 11R18
The authors are indebted to the anonymous referee for his/her valuable suggestions which have helped improving the presentation of this manuscript.
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