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 A262561 The x coordinate of the fundamental unit in the cubic field Q(D^(1/3)): see Comments for precise definition. 3

%I #9 Jun 23 2020 06:17:18

%S -1,-2,-1,1,1,2,-2,-3,1,1,-4,1,1,18,1,1,1,-47,23,-41399,1,3,0,

%T -322461439,1,-367,3742201,613,-7,1,10

%N The x coordinate of the fundamental unit in the cubic field Q(D^(1/3)): see Comments for precise definition.

%C Let D be the n-th cubefree number greater than 1, that is, D = A004709(n), n >= 2.

%C Let F = cubic field Q(D^(1/3)). Let eta be the positive fundamental unit in F. Then eta has a unique representation as eta = x + y*alpha + z*gamma, where (1,alpha,gamma) is the appropriate modified Dedekind basis for F. Then x,y,z are given by A262561, A262562, A262563 respectively.

%C See Sved (1970) for further details. Sved gives a table for all D < 200.

%H Marta Sved, <a href="http://annalesm.elte.hu/annales13-1970/Annales_1970_T-XIII.pdf">Units in pure cubic number fields</a>, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 13 (1970), 141-149.

%Y Cf. A004709, A262562, A262563.

%K sign,more

%O 2,2

%A _N. J. A. Sloane_, Oct 18 2015

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Last modified November 29 03:03 EST 2023. Contains 367422 sequences. (Running on oeis4.)