On a method of solving a class of Diophantine equations

Author:
Charles M. Grinstead

Journal:
Math. Comp. **32** (1978), 936-940

MSC:
Primary 10B20

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 . The method is illustrated by applying it to a set of Diophantine equations.

**[1]**A. Baker,*Linear forms in the logarithms of algebraic numbers. IV*, Mathematika**15**(1968), 204–216. MR**0258756****[2]**A. Baker and H. Davenport,*The equations 3𝑥²-2=𝑦² and 8𝑥²-7=𝑧²*, Quart. J. Math. Oxford Ser. (2)**20**(1969), 129–137. MR**0248079****[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. Kangasabapathy and Tharmambikai Ponnudurai,*The simultaneous Diophantine equations 𝑦²-3𝑥²=-2 and 𝑧²-8𝑥²=-7*, Quart. J. Math. Oxford Ser. (2)**26**(1975), no. 103, 275–278. MR**0387182****[5]**Giovanni Sansone,*Il sistema diofanteo 𝑁+1=𝑥², 3𝑁+1=𝑦², 8𝑁+1=𝑧².*, Ann. Mat. Pura Appl. (4)**111**(1976), 125–151 (Italian). MR**0424672**

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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