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.
KeywordsLattice Point Lattice Line Geometric Method Diophantine Approximation Inhomogeneous Lattice
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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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