The cubics which are differences of two conjugates of an algebraic integer
Toufik Zaimi1
1 King Saud University Dept. of Mathematics P. O. Box 2455 Riyadh 11451, Saudi Arabia
Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 949-953.

On montre qu’un entier algébrique cubique sur un corps de nombres K, de trace nulle est la différence de deux conjugués sur K d’un entier algébrique. On prouve aussi que si N est une extension cubique normale du corps des rationnels, alors tout entier de N de trace zéro est la différence de deux conjugués d’un entier de N si et seulement si la valuation 3-adique du discriminant de N est différente de 4.

We show that a cubic algebraic integer over a number field K, with zero trace is a difference of two conjugates over K of an algebraic integer. We also prove that if N is a normal cubic extension of the field of rational numbers, then every integer of N with zero trace is a difference of two conjugates of an integer of N if and only if the 3-adic valuation of the discriminant of N is not 4.

DOI : 10.5802/jtnb.529
Toufik Zaimi 1

1 King Saud University Dept. of Mathematics P. O. Box 2455 Riyadh 11451, Saudi Arabia 
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Toufik Zaimi. The cubics which are differences of two conjugates of an algebraic integer. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 949-953. doi : 10.5802/jtnb.529. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.529/

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