Geometric Methods in Number Theory
In the proofs of the previous chapters we often used geometrical considerations. We will present one more such proof. Wilson’s theorem (Theorem 2.14) was easily proved in two different ways using congruences. We will now give a proof of it that does not use congruences.
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- 4.In addition to his articles, he wrote two books that thoroughly deal with this subject: Geometrie der Zahlen (Leipzig, 1897) and Diophantische Approximationen (Leipzig, 1907). A modern treatment is given in J.W. S. Cassels: An Introduction to the Geometry of Numbers (Springer, 1959), and further in the encyclopedic work P. Gruber, C.G. Lekkerkerker: Geometry of numbers (North Holland, 1987).Google Scholar
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- 10.This problem appeared on the Miklós Schweizer Memorial Competition in 1964. This is a national mathematics competition in Hungary for high school students. See Matematikai Lapok 16 (1965), pp. 92–113, Problem 4 (in Hungarian) and Contests in Higher Mathematics, G.J. Székely (ed.), Springer, 1996, pp. 5 and 247–249.Google Scholar
- 11.G. Blrkhoff (1914), referred to in H. F. Blichfeldt: Transactions Amer. Math. Soc. 15 (1914), pp. 227–235. W. Scherrer: Math. Annalen 89 (1923), pp. 255–259, and Dissertation, Universität Zürich, 1923. Gy. Hajós: Acta Sei. Math. Szeged, 6 (1934), pp. 224–225.Google Scholar
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