The motivation here is that the `` p '' - torsion in the ideal class group of formula_14 had already been identified by Kummer as the main obstruction to the direct proof of Fermat 's last theorem .
The motivation here was undoubtedly that the formula_4-torsion in the ideal class group of formula_15 had already been identified by Kummer as the main obstacle to the direct proof of Fermat 's last theorem .