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Optimal logarithmic functions for lifting of a solution of an exponential congruence
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I. A. Popovyan
Published/Copyright:
June 28, 2007
This study is devoted to the problem of lifting of a solution of an exponential congruence in rings of integer algebraic numbers. To lift a solution in rings of integer rational numbers, Riesel suggested to use the Fermat quotients apparatus. With their use, the problem reduces to solution of a linear congruence modulo a prime number, and this congruence appears to be irreducible. In this paper we construct analogues of Fermat quotients in rings of integer algebraic numbers which also yield irreducible linear congruences for the problem of lifting of a solution in this case.
Published Online: 2007-06-28
Published in Print: 2007-07-20
Copyright 2007, Walter de Gruyter
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Articles in the same Issue
- The compound Poisson distribution of the number of matches of values of a discrete function of s-tuples in segments of a sequence of random variables
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- Optimal logarithmic functions for lifting of a solution of an exponential congruence
- On the number of independent sets in graphs with fixed independence number
- Homomorphisms and endomorphisms of linear and alinear quasigroups
- On finite groups close to completely factorisable groups
- Non-asymptotic bounds for probabilities of the rank of a random matrix over a finite field
- On representation of k-valued logic functions by a sum of products of subfunctions
- A lower bound for the 4-satisfiability threshold
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