Primitive values of quadratic polynomials in a finite field

Andrew Booker; Stephen Cohen; Nicole Sutherland; Timothy Trudgian

doi:10.1090/mcom/3390

Primitive values of quadratic polynomials in a finite field

Andrew Booker, Stephen Cohen, Nicole Sutherland, Timothy Trudgian

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Abstract

We prove that for all q > 211, there always exists a primitive root g in the finite field F_q such that Q(g) is also a primitive root, where Q(x) = ax² + bx + c is a quadratic polynomial with a; b; c ∈ F_q such that b² — 4ac ≠ 0.

Original language	English
Number of pages	10
Journal	Mathematics of Computation
Early online date	30 Oct 2018
DOIs	https://doi.org/10.1090/mcom/3390
Publication status	E-pub ahead of print - 30 Oct 2018

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abstract = "We prove that for all q > 211, there always exists a primitive root g in the finite field Fq such that Q(g) is also a primitive root, where Q(x) = ax2 + bx + c is a quadratic polynomial with a; b; c ∈ Fq such that b2 — 4ac ≠ 0.",

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AU - Sutherland, Nicole

AU - Trudgian, Timothy

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N2 - We prove that for all q > 211, there always exists a primitive root g in the finite field Fq such that Q(g) is also a primitive root, where Q(x) = ax2 + bx + c is a quadratic polynomial with a; b; c ∈ Fq such that b2 — 4ac ≠ 0.

AB - We prove that for all q > 211, there always exists a primitive root g in the finite field Fq such that Q(g) is also a primitive root, where Q(x) = ax2 + bx + c is a quadratic polynomial with a; b; c ∈ Fq such that b2 — 4ac ≠ 0.

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DO - 10.1090/mcom/3390

M3 - Article (Academic Journal)

SN - 0025-5718

JO - Mathematics of Computation

JF - Mathematics of Computation

ER -

Primitive values of quadratic polynomials in a finite field

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