Tokyo Journal of Mathematics

The Primes for Which an Abelian Cubic Polynomial Splits

James G. HUARD, Blair K. SPEARMAN, and Kenneth S. WILLIAMS

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Abstract

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 $p$, \[ x^3+Ax+B\equiv 0\pmod{p} \text{ has three solutions} \Leftrightarrow p\equiv a_1,\ldots,a_t\pmod{F}. \]

Article information

Source
Tokyo J. Math., Volume 17, Number 2 (1994), 467-478.

Dates
First available in Project Euclid: 1 April 2010

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1270127967

Digital Object Identifier
doi:10.3836/tjm/1270127967

Mathematical Reviews number (MathSciNet)
MR1305814

Zentralblatt MATH identifier
0823.11062

Citation

HUARD, James G.; SPEARMAN, Blair K.; WILLIAMS, Kenneth S. The Primes for Which an Abelian Cubic Polynomial Splits. Tokyo J. Math. 17 (1994), no. 2, 467--478. doi:10.3836/tjm/1270127967. https://projecteuclid.org/euclid.tjm/1270127967


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