Primitive free cubics with specified norm and trace
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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 (not equal 0) and b (primitive) is guaranteed. This is the most delicate case of a general existence theorem whose proof is thereby completed.
Huczynska , S & Cohen , S D 2003 , ' Primitive free cubics with specified norm and trace ' Transactions of the American Mathematical Society , vol 355 , no. 8 , pp. 3099-3116 . DOI: 10.1090/S0002-9947-03-03301-4
Transactions of the American Mathematical Society
(c)2003 American Mathematical Society. First published in Transactions of the American Mathematical Society 355 (2003), available at http://www.ams.org
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