Complete Solution of the Polynomial Version of a Problem of Diophantus

@inproceedings{Dujella2004CompleteSO,
  title={Complete Solution of the Polynomial Version of a Problem of Diophantus},
  author={Andrej Dujella and Clemens Fuchs},
  year={2004}
}
In this paper, we prove that if {a, b, c, d} is a set of four non-zero polynomials with integer coefficients, not all constant, such that the product of any two of its distinct elements plus 1 is a square of a polynomial with integer coefficients, then (a + b − c − d) = 4(ab + 1)(cd + 1). This settles the “strong” Diophantine quintuple conjecture for polynomials with integer coefficients. 

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Showing 1-8 of 8 references

A variation of a problem of Davenport and Diophantus

  • B. W. Jones
  • Quart. J. Math. Oxford Ser.(2)
  • 1976
Highly Influential
6 Excerpts

The equations 3x2−2 = y2 and 8x2−7 = z2

  • A. Baker, H. Davenport
  • Quart. J. Math. Oxford Ser. (2)
  • 1969
Highly Influential
4 Excerpts

On Euler’s solution of a problem of Diophantus

  • J. Arkin, V. E. Hoggatt, E. G. Strauss
  • Fibonacci Quart
  • 1979
2 Excerpts

The equations 3 x 2 − 2 = y 2 and 8 x 2 − 7 = z 2 , Quart

  • H. Davenport
  • . J . Math . Oxford Ser .
  • 1969

A generalised SternBrocot tree from regular Diophantine quadruples , preprint , math

  • B. W. Jones

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