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December 1994 The Primes for Which an Abelian Cubic Polynomial Splits
James G. HUARD, Blair K. SPEARMAN, Kenneth S. WILLIAMS
Tokyo J. Math. 17(2): 467-478 (December 1994). DOI: 10.3836/tjm/1270127967


Let $X^3+AX+B$ be an irreducible abelian cubic polynomial in $Z[X]$. We determine explicitly integers $a_1,\ldots,a_t$, $F$ such that, except for finitely many primes $p$, \[ x^3+Ax+B\equiv 0\pmod{p} \text{ has three solutions} \Leftrightarrow p\equiv a_1,\ldots,a_t\pmod{F}. \]


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James G. HUARD. Blair K. SPEARMAN. Kenneth S. WILLIAMS. "The Primes for Which an Abelian Cubic Polynomial Splits." Tokyo J. Math. 17 (2) 467 - 478, December 1994.


Published: December 1994
First available in Project Euclid: 1 April 2010

zbMATH: 0823.11062
MathSciNet: MR1305814
Digital Object Identifier: 10.3836/tjm/1270127967

Rights: Copyright © 1994 Publication Committee for the Tokyo Journal of Mathematics

Vol.17 • No. 2 • December 1994
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