A note on integral clock triangles.
J. MacLeod, Allan (2008)
Annales Mathematicae et Informaticae
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J. MacLeod, Allan (2008)
Annales Mathematicae et Informaticae
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Bremner, Andrew (2006)
Annales Mathematicae et Informaticae
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Lahyane, Mustapha (2002)
International Journal of Mathematics and Mathematical Sciences
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M. R. Gonzalez-Dorrego (2006)
Annales Polonici Mathematici
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Let k be an algebraically closed field of characteristic 0. Let C be an irreducible nonsingular curve in ℙⁿ such that 3C = S ∩ F, where S is a hypersurface and F is a surface in ℙⁿ and F has rational triple points. We classify the rational triple points through which such a curve C can pass (Theorem 1.8), and give an example (1.12). We only consider reduced and irreducible surfaces.
Matt DeLong (2002)
Acta Arithmetica
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T. G. Berry (1992)
Acta Arithmetica
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Petulante, Nelson, Kaja, Ifeoma (2000)
International Journal of Mathematics and Mathematical Sciences
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Dimitrios Poulakis (2003)
Acta Arithmetica
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Tatiana Lavrinenko (2002)
Revue d'histoire des mathématiques
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This article concerns the problem of solving diophantine equations in rational numbers. It traces the way in which the 19th century broke from the centuries-old tradition of the purely algebraic treatment of this problem. Special attention is paid to Sylvester’s work “On Certain Ternary Cubic-Form Equations” (1879–1880), in which the algebraico-geometrical approach was applied to the study of an indeterminate equation of third degree.
N. Mohan Kumar (1981/82)
Inventiones mathematicae
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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.
Soukenka, Martin
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J. Achari (1978)
Matematički Vesnik
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