On the Diophantine equation

Author:
Leo J. Alex

Journal:
Math. Comp. **44** (1985), 267-278

MSC:
Primary 11D61

DOI:
https://doi.org/10.1090/S0025-5718-1985-0771050-0

MathSciNet review:
771050

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Abstract | References | Similar Articles | Additional Information

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.

**[1]**L. J. Alex, "Diophantine equations related to finite groups,"*Comm. Algebra*, v. 4, 1976, pp. 77-100. MR**0424675 (54:12634)****[2]**L. J. Alex, "The Diophantine equation ,"*Notices Amer. Math. Soc.*, v. 26, 1979, p. A-454, Abstract #768-10-13.**[3]**L. J. Alex, "Simple groups and a Diophantine equation,"*Pacific J. Math.*, v. 104, no. 2, 1983, pp. 257-262. 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. 321-331. MR**702828 (84j:10015)****[5]**J. L. Brenner & L. L. Foster, "Exponential Diophantine equations,"*Pacific J. Math.*, v. 101, no. 2, 1982, pp. 263-301. MR**675401 (83k:10035)****[6]**E. Dubois & G. Rhin, "Sur la majoration de formes linéaires à coefficients algébriques réels et*p*-adiques. Démonstration d'une conjecture de K. Mahler,"*C. R. Acad. Sci. Paris Ser. A*, v. 282, 1976, pp. 1211-1214. MR**0429783 (55:2793)****[7]**H. P. Schlickewei, "Über die diophantische Gleichung ,"*Acta Arith.*, v. 33, 1977, pp. 183-185. MR**0439747 (55:12633)****[8]**H. G. Senge & E. G. Straus, "PV-numbers and sets of multiplicity,"*Period. Math. Hungar.*v. 3, 1973, pp. 93-100. MR**0340185 (49:4941)****[9]**R. Tijdeman, "Diophantine equations (Approximation methods)." (To appear.)**[10]**Chen-Te Yen, "Some exponential Diophantine equations." (To appear.) MR**794914 (86j:11031)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1985-0771050-0

Keywords:
Exponential Diophantine equation

Article copyright:
© Copyright 1985
American Mathematical Society