Turkish Journal of Mathematics
DOI
10.3906/mat-1911-88
Abstract
Let $K$ be a totally real number field with narrow class number one and $O_K$ be its ring of integers. We prove that there is a constant $B_K$ depending only on $K$ such that for any prime exponent $p>B_K$ the Fermat type equation $x^p+y^p=z^2$ with $x,y,z\in O_K$ does not have certain type of solutions. Our main tools in the proof are modularity, level lowering, and image of inertia comparisons.
First Page
1197
Last Page
1211
Recommended Citation
IŞIK, ERMAN; KARA, YASEMİN; and KARAKURT, EKİN ÖZMAN
(2020)
"On ternary Diophantine equations of signature $(p,p,2)$ over number fields,"
Turkish Journal of Mathematics: Vol. 44:
No.
4, Article 9.
https://doi.org/10.3906/mat-1911-88
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss4/9