The Order of A Root of x<SUP>p</SUP>-x-1 over F<SUB>p</SUB>

SHI Jian-yi; WANG Zhen-hua

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Issue 2

Jun. 2004

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Article Navigation > Journal of East China Normal University (Natural Sciences) > 2004 > (2): 1-4,23

SHI Jian-yi, WANG Zhen-hua. The Order of A Root of xp-x-1 over Fp[J]. Journal of East China Normal University (Natural Sciences), 2004, (2): 1-4,23.

Citation:

SHI Jian-yi, WANG Zhen-hua. The Order of A Root of x^p-x-1 over F_p[J]. Journal of East China Normal University (Natural Sciences), 2004, (2): 1-4,23.

SHI Jian-yi, WANG Zhen-hua. The Order of A Root of xp-x-1 over Fp[J]. Journal of East China Normal University (Natural Sciences), 2004, (2): 1-4,23.

Citation:

SHI Jian-yi, WANG Zhen-hua. The Order of A Root of x^p-x-1 over F_p[J]. Journal of East China Normal University (Natural Sciences), 2004, (2): 1-4,23.

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The Order of A Root of x^p-x-1 over F_p

1.
Institute of Network Information Security, East China Normal University, Shanghai 200062, China

More Information

Corresponding author: SHI Jian-yi
Received Date: 2002-04-10
Rev Recd Date: 2003-06-27
Publish Date: 2004-06-25

Abstract

Abstract

The present paper is concerned with the order o(αp) of a root αp of the polynomial xp-x-1 over a prime field Fp. We propose a conjecture that o(αp)=mp:=(pp-1)/(p-1) for any prime p. Then we introduce two methods to verify the conjecture in certain cases.
- polynomialfinite fieldorder of a root,