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

Isik, Erman; Kara, Yasemin; Ozman, Ekin


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        "name": "Isik, Erman"
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        "affiliation": "Bogazici Univ, Fac Arts & Sci, Dept Math, Istanbul, Turkey", 
        "name": "Kara, Yasemin"
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      {
        "affiliation": "Bogazici Univ, Fac Arts & Sci, Dept Math, Istanbul, Turkey", 
        "name": "Ozman, Ekin"
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    "description": "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. O-K does not have certain type of solutions. Our main tools in the proof are modularity, level lowering, and image of inertia comparisons.", 
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