JP Journal of Algebra, Number Theory and Applications
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Abstract: The
final computational step is provided that
secures the theorem that, for any integer n³
7, there exists a primitive polynomial over any
finite field Fq
whose first three coefficients are arbitrarily
prescribed elements of Fq.
This builds on theoretical work of Fan Shuqin
and Han Wenbao, especially in the case when Fq
has characteristic 2 or 3, and of D. Mills when
the characteristic is at least 5. In particular,
a conjecture of Mills is established.
Keywords and phrases: primitive
polynomial, finite field, fixed coefficients.
