The Order of A Root of xp-x-1 over Fp
Jian-yi Shi, Zhenhua Wang · Huadong Shifan Daxue xuebao. Ziran kexue ban · 2004
The present paper is concerned with the order o(ap) of a root ap of the polynomial xp - x- 1 over a prime field Fp. We propose a conjecture that o(ap) = mp: = (pp - 1)/(p- 1) for any prime p. Then we introduce two methods to verify the conjecture in certain cases.