Solutions to xyz = 1 and x+y+z = k in algebraic integers of small degree, I

• Autorzy: H. G. Grundman , L. L. Hall-Seelig
• Języki publikacji: EN

Abstrakty

EN

Let k ∈ ℤ be such that $|𝓔_k(ℚ )| = 3$, where $𝓔_k: y² = 1 - 2kx + k²x² - 4x³$. We determine all solutions to xyz = 1 and x + y + z = k in integers of number fields of degree at most four over ℚ.

Kategorie tematyczne

• 11D25: Cubic and quartic equations
• 11R16: Cubic and quartic extensions
• 11G05: Elliptic curves over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 162
• Numer: 4
• Strony: 381-392

Daty

wydano

2014

Twórcy

autor

H. G. Grundman

• Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, U.S.A.

autor

L. L. Hall-Seelig

• Department of Mathematics, Merrimack College, North Andover, MA 01845, U.S.A.

Identyfikatory

DOI

10.4064/aa162-4-5