On the Diophantine equation $1+2^ a=3^ b5^ c+2^ d3^ e5^ f$

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: In this paper the Diophantine equation $1 + {2^a} = {3^b}{5^c} + {2^d}{3^e}{5^f}$, where *a, b, c, d, e* and *f* are nonnegative integers, is solved. The related equations $1 + {3^a} = {2^b}{5^c} + {2^d}{3^e}{5^f}$ and $1 + {5^a} = {2^b}{3^c} + {2^d}{3^e}{5^f}$ are also solved. This work is related to and extends recent work of L. L. Foster, J. L. Brenner, and the author.

- Leo J. Alex,
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*Notices Amer. Math. Soc.*, v. 26, 1979, p. A-454, Abstract #768-10-13.

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Keywords:
Exponential Diophantine equation

Article copyright:
© Copyright 1985
American Mathematical Society