Vol. 2, No. 4, 2009

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A complete classification of $\mathbb{Z}_{p}$-sequences corresponding to a polynomial

Leonard Huang

Vol. 2 (2009), No. 4, 411–418

Let p be a prime number and set p = p. A p-sequence is a function S : p. Let be the set {P [X]P() }. We prove that the set of sequences of the form (P(n)( mod p))n, where P , is precisely the set of periodic p-sequences with period equal to a p-power. Given a p-sequence, we will also determine all P that correspond to the sequence according to the manner above.

$\mathbb{Z}_p$-sequences, polynomials, free abelian group
Mathematical Subject Classification 2000
Primary: 11B83
Received: 25 October 2008
Revised: 15 September 2009
Accepted: 15 September 2009
Published: 28 October 2009

Communicated by Andrew Granville
Leonard Huang
School of Physical and Mathematical Sciences
Nanyang Technological University
21 Nanyang Link