Gras's strong Fermat's last theorem conjecture

Let $p$ be an odd prime, set $K=$\mathbb Q$(\zeta)$ and $\mathfrak p=(\zeta-1)$\mathbb Z$[\zeta]$. For coprime integers $u,v$, let $\delta\geq 0$ and let $\mathfrak w_1$ be an integral ideal of $K$. Strong Fermat's last theorem conjecture. The equation

(u+v\zeta)\text{\mathbb Z}[\zeta]=\mathfrak p^\delta\mathfrak w_1^p

has no solution for $p>3$, except when $u+v\zeta=\pm1,\pm\zeta,\pm(1+\zeta)$, or $\pm(1-\zeta)$. This is a strong form of the second case of Fermat's last theorem, and the source attributes it to G. Gras; its status is not specified here.