On the Diophantine equation
Author:
Leo J. Alex
Journal:
Math. Comp. 44 (1985), 267278
MSC:
Primary 11D61
MathSciNet review:
771050
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Abstract: In this paper the Diophantine equation , where a, b, c, d, e and f are nonnegative integers, is solved. The related equations and are also solved. This work is related to and extends recent work of L. L. Foster, J. L. Brenner, and the author.
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L. J. Alex, "The Diophantine equation ," Notices Amer. Math. Soc., v. 26, 1979, p. A454, Abstract #7681013.
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Leo
J. Alex, Simple groups and a Diophantine equation, Pacific J.
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Leo
J. Alex and Lorraine
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1+2^{𝑎}=𝑝^{𝑏}𝑞^{𝑐}+2^{𝑑}𝑝^{𝑒}𝑞^{𝑓},
Rocky Mountain J. Math. 13 (1983), no. 2,
321–331. MR
702828 (84j:10015), http://dx.doi.org/10.1216/RMJ1983132321
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J.
L. Brenner and Lorraine
L. Foster, Exponential Diophantine equations, Pacific J. Math.
101 (1982), no. 2, 263–301. MR 675401
(83k:10035)
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Eugène
Dubois and Georges
Rhin, Sur la majoration de formes linéaires à
coefficients algébriques réels et 𝑝adiques.
Démonstration d’une conjecture de K. Mahler, C. R. Acad.
Sci. Paris Sér. AB 282 (1976), no. 21, Ai,
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𝑥₁+𝑥₂\cdots+𝑥_{𝑛}=0,
Acta Arith. 33 (1977), no. 2, 183–185. MR 0439747
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93–100. Collection of articles dedicated to the memory of
Alfréd Rényi, II. MR 0340185
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R. Tijdeman, "Diophantine equations (Approximation methods)." (To appear.)
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Chen
Te Yen, Some exponential Diophantine equations, Bull. Inst.
Math. Acad. Sinica 13 (1985), no. 1, 49–92. MR 794914
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 [1]
 L. J. Alex, "Diophantine equations related to finite groups," Comm. Algebra, v. 4, 1976, pp. 77100. MR 0424675 (54:12634)
 [2]
 L. J. Alex, "The Diophantine equation ," Notices Amer. Math. Soc., v. 26, 1979, p. A454, Abstract #7681013.
 [3]
 L. J. Alex, "Simple groups and a Diophantine equation," Pacific J. Math., v. 104, no. 2, 1983, pp. 257262. MR 684288 (84c:20024)
 [4]
 L. J. Alex & L. L. Foster, "On Diophantine equations of the form ," Rocky Mountain J. Math., v. 13, no. 2, 1983, pp. 321331. MR 702828 (84j:10015)
 [5]
 J. L. Brenner & L. L. Foster, "Exponential Diophantine equations," Pacific J. Math., v. 101, no. 2, 1982, pp. 263301. MR 675401 (83k:10035)
 [6]
 E. Dubois & G. Rhin, "Sur la majoration de formes linéaires à coefficients algébriques réels et padiques. Démonstration d'une conjecture de K. Mahler," C. R. Acad. Sci. Paris Ser. A, v. 282, 1976, pp. 12111214. MR 0429783 (55:2793)
 [7]
 H. P. Schlickewei, "Über die diophantische Gleichung ," Acta Arith., v. 33, 1977, pp. 183185. MR 0439747 (55:12633)
 [8]
 H. G. Senge & E. G. Straus, "PVnumbers and sets of multiplicity," Period. Math. Hungar. v. 3, 1973, pp. 93100. MR 0340185 (49:4941)
 [9]
 R. Tijdeman, "Diophantine equations (Approximation methods)." (To appear.)
 [10]
 ChenTe Yen, "Some exponential Diophantine equations." (To appear.) MR 794914 (86j:11031)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198507710500
PII:
S 00255718(1985)07710500
Keywords:
Exponential Diophantine equation
Article copyright:
© Copyright 1985
American Mathematical Society
