Solution of Nathanson’s exponential congruence
HTML articles powered by AMS MathViewer
- by Samuel S. Wagstaff PDF
- Math. Comp. 33 (1979), 1097-1100 Request permission
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.References
- M. B. Nathanson, An exponential congruence of Mahler, Amer. Math. Monthly 79 (1972), 55–57. MR 300973, DOI 10.2307/2978128
- A. J. Van der Poorten, Linear forms in logarithms in the $p$-adic case, Transcendence theory: advances and applications (Proc. Conf., Univ. Cambridge, Cambridge, 1976) Academic Press, London, 1977, pp. 29–57. MR 0498418
- A. Schinzel, On two theorems of Gelfond and some of their applications, Acta Arith 13 (1967/1968), 177–236. MR 0222034, DOI 10.4064/aa-13-2-177-236
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Math. Comp. 33 (1979), 1097-1100
- MSC: Primary 10A10
- DOI: https://doi.org/10.1090/S0025-5718-1979-0528063-0
- MathSciNet review: 528063