1. On the order of modulo , on average.
- Author
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Kim, Sungjin
- Subjects
- *
INTEGERS , *MATHEMATICAL constants , *NUMBER theory , *ARITHMETIC mean , *MULTIPLICATION - Abstract
Let be an integer. Denote by the multiplicative order of modulo integer . We prove that there is a positive constant such that if , then where It was known for in [P. Kurlberg and C. Pomerance, On a problem of Arnold: The average multiplicative order of a given integer, Algebra Number Theory 7 (2013) 981-999] in which they refer to [F. Luca and I. E. Shparlinski, Average multiplicative orders of elements modulo , Acta Arith. 109(4) (2003) 387-411. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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