Arithmetical sequences for the exponents of composite Mersenne numbers

Simon Davis
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 20, 2014, Number 1, Pages 19—26
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Simon Davis
Research Foundation of Southern California
8837 Villa La Jolla Drive #13595
La Jolla, CA 92039, United States

Abstract

Arithmetical sequences for the exponents of composite Mersenne numbers are obtained from partitions into consecutive integers, and congruence relations for products of two Mersenne numbers suggest the existence of infinitely many composite integers of the form 2p − 1 with p prime. A lower probability for the occurrence of composite Mersenne numbers in arithmetical sequences is given.

Keywords

  • Composite Mersenne numbers
  • Exponents in arithmetical sequences

AMS Classification

  • 11B83
  • 11N13
  • 11P83

References

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Cite this paper

APA

Davis, S. (2014). Arithmetical sequences for the exponents of composite Mersenne numbers. Notes on Number Theory and Discrete Mathematics, 20(1), 19-26.

Chicago

Davis, Simon. “Arithmetical Sequences for the Exponents of Composite Mersenne Numbers.” Notes on Number Theory and Discrete Mathematics 20, no. 1 (2014): 19-26.

MLA

Davis, Simon. “Arithmetical Sequences for the Exponents of Composite Mersenne Numbers.” Notes on Number Theory and Discrete Mathematics 20.1 (2014): 19-26. Print.

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