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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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Keywords: Exponential congruence
Article copyright: © Copyright 1979 American Mathematical Society