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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Small two-variable exponential Diophantine equations

Author: Robert Styer
Journal: Math. Comp. 60 (1993), 811-816
MSC: Primary 11D61
MathSciNet review: 1160277
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Abstract: We examine exponential Diophantine equations of the form $ a{b^x} = c{d^y} + e$. Consider $ a \leq 50$, $ c \leq 50$, $ \vert e\vert\; \leq 1000$, and b and d from the set of primes 2, 3, 5, 7, 11, and 13. Our work proves that no equation with parameters in these ranges can have solutions with $ x > 18$. Our algorithm formalizes and extends a method used by Guy, Lacampagne, and Selfridge in 1987.

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Article copyright: © Copyright 1993 American Mathematical Society

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