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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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{
  "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. O-K does not have certain type of solutions. Our main tools in the proof are modularity, level lowering, and image of inertia comparisons.", 
  "author": [
    {
      "family": "Isik", 
      "given": " Erman"
    }, 
    {
      "family": "Kara", 
      "given": " Yasemin"
    }, 
    {
      "family": "Ozman", 
      "given": " Ekin"
    }
  ], 
  "container_title": "TURKISH JOURNAL OF MATHEMATICS", 
  "id": "10545", 
  "issue": "4", 
  "issued": {
    "date-parts": [
      [
        2020, 
        1, 
        1
      ]
    ]
  }, 
  "page": "1197-1211", 
  "title": "On ternary Diophantine equations of signature (p, p, 2) over number fields", 
  "type": "article-journal", 
  "volume": "44"
}
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