Pell-type equations and class number of the maximal real subfield of a cyclotomic field

Abstract

We investigate the solvability of the Diophantine equation $x^2-m{y}^2=\pm p$ 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 bigger than $1$.

Accepted for publication in The Ramanujan Journal, 2017