Small two-variable exponential Diophantine equations
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- by Robert Styer PDF
- Math. Comp. 60 (1993), 811-816 Request permission
Abstract:
We examine exponential Diophantine equations of the form $a{b^x} = c{d^y} + e$. Consider $a \leq 50$, $c \leq 50$, $|e|\; \leq 1000$, 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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 60 (1993), 811-816
- MSC: Primary 11D61
- DOI: https://doi.org/10.1090/S0025-5718-1993-1160277-9
- MathSciNet review: 1160277