Modular forms and class number congruences
Antone Costa (1992)
Acta Arithmetica
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Antone Costa (1992)
Acta Arithmetica
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Robertson, John P. (2009)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Maohua Le (1991)
Colloquium Mathematicae
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Khosroshvili, D. (1998)
Georgian Mathematical Journal
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Henryk Iwaniec, Ritabrata Munshi (2010)
Journal de Théorie des Nombres de Bordeaux
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We give non-trivial upper bounds for the number of integral solutions, of given size, of a system of two quadratic form equations in five variables.
Wayne McDaniel (1993)
Colloquium Mathematicae
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J. Browkin, A. Schinzel (1995)
Colloquium Mathematicae
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W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers (k = 1, 2,...) is of the form n - φ(n).
Lewittes, Joseph, Kolyvagin, Victor (2010)
The New York Journal of Mathematics [electronic only]
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Yasushige Watase (2014)
Formalized Mathematics
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This article provides a formalized proof of the so-called “the four-square theorem”, namely any natural number can be expressed by a sum of four squares, which was proved by Lagrange in 1770. An informal proof of the theorem can be found in the number theory literature, e.g. in [14], [1] or [23]. This theorem is item #19 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/.