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On a method of solving a class of Diophantine equations


Author: Charles M. Grinstead
Journal: Math. Comp. 32 (1978), 936-940
MSC: Primary 10B20
DOI: https://doi.org/10.1090/S0025-5718-1978-0491480-0
MathSciNet review: 0491480
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Abstract: An elementary method for solving simultaneous Diophantine equations is given. This method will in general lead quickly to a solution-free region on the order of $ 1 < x < {10^{{{10}^{50}}}}$. The method is illustrated by applying it to a set of Diophantine equations.


References [Enhancements On Off] (What's this?)

  • [1] A. BAKER, "Linear forms in the logarithms of algebraic numbers," Mathematika, v. 15, 1968, pp. 204-216. MR 0258756 (41:3402)
  • [2] A. BAKER & H. DAVENPORT, "The equations $ 3{x^2} - 2 = {y^2}$ and $ 8{x^2} - 7 = {z^2}$," Quart. J. Math., v. 20, 1969, pp. 129-137. MR 0248079 (40:1333)
  • [3] M. GARDNER, "On the patterns and the unusual properties of figurate numbers," Sci. Amer., v. 231, no. 1, 1974, pp. 116-121.
  • [4] P. KANAGASABAPATHY & T. PONNUDURAI, "The simultaneous diophantine equations $ {y^2} - 3{x^2} = - 2$ and $ {z^2} - 8{x^2} = - 7$," Quart. J. Math., v. 26, 1975, pp. 275-278. MR 0387182 (52:8027)
  • [5] GIOVANNI SANSONE, "Il sistema diofanteo $ N + 1 = {x^2}$, $ 3N + 1 = {y^2}$, $ 8N + 1 = {z^2}$," Ann. Mat. Pura Appl. (4), v. 111, 1976, pp. 125-151. MR 0424672 (54:12631)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0491480-0
Keywords: Diophantine equations, linear recurrent sequences
Article copyright: © Copyright 1978 American Mathematical Society

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