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

Azizul Hoque, Kalyan Chakraborty

Published 2017-10-26Version 1

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 bigger than $1$.