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

The Ljunggren equation revisited

Konstantinos A. Draziotis (2007)

Colloquium Mathematicae

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We study the Ljunggren equation Y² + 1 = 2X⁴ using the "multiplication by 2" method of Chabauty.

The real field with the rational points of an elliptic curve

Ayhan Günaydın, Philipp Hieronymi (2011)

Fundamenta Mathematicae

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We consider the expansion of the real field by the group of rational points of an elliptic curve over the rational numbers. We prove a completeness result, followed by a quantifier elimination result. Moreover we show that open sets definable in that structure are semialgebraic.