Undecidable diophantine equations

  title={Undecidable diophantine equations},
  author={James P. Jones},
  journal={Bulletin of the American Mathematical Society},
  • 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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1 Hilbert ’ s Tenth Problem
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  • 1994
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  • A. Baker
  • Mathematics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1968
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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Baker , Contributions to the theory of diophantine equations . I , Philos
  • 1968
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  • 1978
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  • sets, J. Symbolic Logic
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