On the cycle structure of repeated exponentiation modulo a prime

JOURNAL OF NUMBER THEORY

卷:107

Article

Chou, WS ; Shparlinski, IE

关键词: repeated powering;    cycle structure;    primes in arithmetic progressions;   

DOI  :  10.1016/j.jnt.2004.04.005

来源: Elsevier

【 摘 要 】

In a recent work, Shallit and Vasiga have obtained several results about tails and cycles in orbits of repeated squaring. Some of these results have been based on the Extended Riemann Hypothesis. Here, we extend their result to repeated exponentiation with any fixed exponent e and also show that in fact classical unconditional results about the distribution of primes in arithmetic progressions, combined with very elementary arguments, are quite sufficient to generalise and give an unconditional proof of their asymptotic formulas. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free