Kummer proved that there are no non-trivial solutions to the fermat Fermat equation FTL(n)FLT(n): $x^n + y^n = z^n$ with $n natural > 2 2$ natural and x,y,z $x,y,z$ elements of a regular cyclotomic ring of integers $K$.

I am looking for non-trivial solutions to the Fermat equation FLT(p) in the cyclotomic integer ring $\mathbb{Z}[\zeta_{p}]$ for irregular primes p or any information about how the solutions must be (as a step toward constructing them).

George Lowther pointed out in an earlier discussion that by Kolyvagin's criterion any solution in $\mathbb{Z}[\zeta_{37}]$ must be in the second case.

Kummer proved that there are zero no non-trivial solutions to the fermat equation FTL(n): $x^n + y^n = z^n$ with n natural > 2 and x,y,z elements of a regular cyclotomic ring of integers .$K$.

I am looking for non-trivial solutions to the Fermat equation FLT(p) in an irregular the cyclotomic integer ring $\mathbb{Z}[\zeta_{p}]$ for irregular primes p or any information about how the solutions must be (as a step toward constructing them).

George Lowther pointed out in an earlier discussion that by Kolyvagin's criterion any solution in $\mathbb{Q}(\zeta_{37})$ \mathbb{Z}[\zeta_{37}]$ must be in the second case.

Kummer proved that there are zero non-trivial solutions to the fermat equation $x^n + y^n = z^n$ with n natural > 2 and x,y,z elements of a regular cyclotomic ring of integers.

I am looking for non-trivial solutions to the Fermat equation in an irregular cyclotomic integer ring or any information about how the solutions must be (as a step toward constructing them).

George Lowther pointed out in an earlier discussion that by Kolyvagin's criterion any solution in $\mathbb{Q}(\zeta_{37})$ must be in the second case.