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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Solution of Nathanson's exponential congruence


Author: Samuel S. Wagstaff
Journal: Math. Comp. 33 (1979), 1097-1100
MSC: Primary 10A10
MathSciNet review: 528063
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Abstract: The exponential congruence $ {5^n} \equiv 2\;\pmod {3^n}$ has no solution $ n > 1$. This result is proved by using a theorem of van der Poorten to produce an upper bound for the size of such solutions n which is within range of machine verification, and then checking that no n below this bound satisfies the congruence.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1979-0528063-0
PII: S 0025-5718(1979)0528063-0
Keywords: Exponential congruence
Article copyright: © Copyright 1979 American Mathematical Society