Abstract
We examine exponential Diophantine equations of the form a b x = c d y + e a{b^x} = c{d^y} + e . Consider a ≤ 50 a \leq 50 , c ≤ 50 c \leq 50 , | e | ≤ 1000 |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 x > 18 . Our algorithm formalizes and extends a method used by Guy, Lacampagne, and Selfridge in 1987.
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