On rational automorphs of quadratic forms
J. Wójcik (1974)
Colloquium Mathematicae
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J. Wójcik (1974)
Colloquium Mathematicae
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T.M.K. Davison (1987)
Aequationes mathematicae
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Svetozar Kurepa (1987)
Aequationes mathematicae
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Amir Jafari, Farhood Rostamkhani (2022)
Czechoslovak Mathematical Journal
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For a ternary quadratic form over the rational numbers, we characterize the set of rational numbers represented by that form over the rational numbers. Consequently, we reprove the classical fact that any positive definite integral ternary quadratic form must fail to represent infinitely many positive integers over the rational numbers. Our proof uses only the quadratic reciprocity law and the Hasse-Minkowski theorem, and is elementary.
C.E. Nelson (1974)
Aequationes mathematicae
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Hoffmann, Detlev W. (1996)
Documenta Mathematica
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T.M.K. Davison (1980)
Aequationes mathematicae
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G. Rousseau (1987)
Aequationes mathematicae
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Lerna Pehlivan, Kenneth S. Williams (2015)
Acta Arithmetica
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Ricardo Baeza (1979)
Mémoires de la Société Mathématique de France
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Inventiones mathematicae
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Pete L. Clark, William C. Jagy (2014)
Acta Arithmetica
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We study ADC quadratic forms and Euclidean quadratic forms over the integers, obtaining complete classification results in the positive case.