Abstract :
Letlbe any odd prime andζanlth root of unity. LetCl(i)be the eigenspace of the ideal class group ofQ(ζ) corresponding toωi, ωbeing the Teichmuller character. We prove that if the order ofCl(3)islh3, thenxln+yln+zln=0 has no solutions withldoes not dividexyz,ngreater-or-equal, slantedmax(1, h3).
