The equation xyz = x + y + z = 1 in integers of a cubic field.

Andrew Bremner

Displaying similar documents to “The equation xyz = x + y + z = 1 in integers of a cubic field.”

Simplest Cubic Fields.

Franz Lemmermeyer, Attila Pethö (1995)

Manuscripta mathematica

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On the fundamental units of some cubic orders generated by units

Jun Ho Lee, Stéphane R. Louboutin (2014)

Acta Arithmetica

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Let ϵ be a totally real cubic algebraic unit. Assume that the cubic number field ℚ(ϵ) is Galois. Let ϵ, ϵ' and ϵ'' be the three real conjugates of ϵ. We tackle the problem of whether {ϵ,ϵ'} is a system of fundamental units of the cubic order ℤ[ϵ,ϵ',ϵ'']. Given two units of a totally real cubic order, we explain how one can prove that they form a system of fundamental units of this order. Several explicit families of totally real cubic orders defined by parametrized families of cubic...

Some reults on fundamental units in cubic fields.

H.C. Williams (1976)

Journal für die reine und angewandte Mathematik

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Generators and integral points on twists of the Fermat cubic

Yasutsugu Fujita, Tadahisa Nara (2015)

Acta Arithmetica

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We study integral points and generators on cubic twists of the Fermat cubic curve. The main results assert that integral points can be in a system of generators in the case where the Mordell-Weil rank is at most two. As a corollary, we explicitly describe the integral points on the curve.