A Note on Distribution of Primitive Roots in a Finite Field
  
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Wang Jun Institute of Appl . Math. Dalian Univ. of Tech. 
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Abstract:
      Let f1(x) , …,fr(x) denote quadratfree polynomials over GF(q) that are relatively prime in pairs and of degree≥1. We have proved that if q≥(k-1)2(2rω(q-1)-1)2, then all the fi(ξ) are primitive roots of GF(q) for some ξ∈GF(q), where k =degf1 … degfr . With extending the results obtained by Wang Juping, Sun Qi and Han Wenbao respectively, we have also given a quantitative analysis of Carlitz's result.
Citation:
DOI:10.3770/j.issn:1000-341X.1990.04.028
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