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Primitive free cubics with specified norm and trace
Authors:Sophie Huczynska  Stephen D Cohen
Institution:Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland ; Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
Abstract:The existence of a primitive free (normal) cubic $x^3-ax^2+cx-b$ over a finite field $F$ with arbitrary specified values of $a$ ($\neq 0$) and $b$ (primitive) is guaranteed. This is the most delicate case of a general existence theorem whose proof is thereby completed.

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