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 $p$, \[ x^3+Ax+B\equiv 0\pmod{p} \text{ has three solutions} \Leftrightarrow p\equiv a_1,\ldots,a_t\pmod{F}. \]
Citation
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. https://doi.org/10.3836/tjm/1270127967
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