"On ternary Diophantine equations of signature $(p,p,2)$ over number fi" by ERMAN IŞIK, YASEMİN KARA et al.

Turkish Journal of Mathematics

Article Title

On ternary Diophantine equations of signature $(p,p,2)$ over number fields

Authors

ERMAN IŞIK
YASEMİN KARA
EKİN ÖZMAN KARAKURT

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

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