Undecidable diophantine equations

@article{Jones1980UndecidableDE,
  title={Undecidable diophantine equations},
  author={James P. Jones},
  journal={Bulletin of the American Mathematical Society},
  year={1980},
  volume={3},
  pages={859-862}
}
  • James P. Jones
  • Published 1 September 1980
  • Mathematics
  • Bulletin of the American Mathematical Society
In 1900 Hubert asked for an algorithm to decide the solvability of all diophantine equations, P(x1, . . . , xv) = 0, where P is a polynomial with integer coefficients. In special cases of Hilbert's tenth problem, such algorithms are known. Siegel [7] gives an algorithm for all polynomials P(xx, . . . , xv) of degree < 2. From the work of A. Baker [1] we know that there is also a decision procedure for the case of homogeneous polynomials in two variables, P(x, y) = c. The first steps toward the… 
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An effective algorithm is established for solving in integers x, y any Diophantine equation of the type/(x, y) = m, where/ denotes an irreducible binary form with integer coefficients and degree at
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DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen,
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