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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
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.

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Keywords: Exponential Diophantine equation
Article copyright: © Copyright 1985 American Mathematical Society