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

 

On Fermat's quotient, base two


Author: D. H. Lehmer
Journal: Math. Comp. 36 (1981), 289-290
MSC: Primary 10-04
MathSciNet review: 595064
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper extends the search for solutions of the congruence

$\displaystyle {2^{p - 1}} - 1 \equiv 0\quad \pmod {p^2}$

to the limit $ p < 6 \cdot {10^9}$. No solution, except the well-known $ p = 1093$ and $ p = 3511$, was found.

References [Enhancements On Off] (What's this?)

  • [1] J. Brillhart, J. Tonascia, and P. Weinberger, On the Fermat quotient, Computers in number theory (Proc. Sci. Res. Council Atlas Sympos. No. 2, Oxford, 1969) Academic Press, London, 1971, pp. 213–222. MR 0314736 (47 #3288)
  • [2] A. Wieferich, "Zum letzen Fermatschen Theorem," J.für Math., v. 136, 1909, pp. 293-302.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1981-0595064-5
PII: S 0025-5718(1981)0595064-5
Article copyright: © Copyright 1981 American Mathematical Society