Wieferich's criterion for Fermat's Last Theorem
A mistake they made is assuming $q_p(s) \equiv q_p(u) \equiv 0 \pmod p$, since $s^{p - 1} \equiv 1/s \pmod {p^2}$.
A mistake they made is assuming $q_p(s) \equiv q_p(u) \equiv 0 \pmod p$, since $s^{p - 1} \equiv 1/s \pmod {p^2}$.