Necessary and sufficient conditions on q ensure every irreducible x² + b x + c (b ≠ 0, c primitive) is primitive over F_q, plus a new infinite family of fields where degree-2 primitive polynomials are easy to identify.
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Necessary and sufficient conditions on the order of a finite field $\mathbb{F}_q$ for the easy identification of primitive polynomials of degree 2
Necessary and sufficient conditions on q ensure every irreducible x² + b x + c (b ≠ 0, c primitive) is primitive over F_q, plus a new infinite family of fields where degree-2 primitive polynomials are easy to identify.