A Higher-Rank Mersenne Problem

Authors:
Graham Everest;Peter Rogers;Thomas Ward
Affiliations:
-;-;-
Venue:
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Year:
2002

Citing 2
Cited 0

Sequences of numbers generated by addition in formal groups and new primality and factorization tests

Advances in Applied Mathematics
The new mersenne conjecture

American Mathematical Monthly

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Abstract

The classical Mersenne problem has been a stimulating challenge to number theorists and computer scientists for many years. After briefly reviewing some of the natural settings in which this problem appears as a special case, we introduce an analogue of the Mersenne problem in higher rank, in both a classical and an elliptic setting. Numerical evidence is presented for both cases, and some of the difficulties involved in developing even a heuristic understanding of the problem are discussed.