History of the Theory of Numbers: Diophantine AnalysisCourier Corporation, 17 oct. 2013 - 832 pages The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms. Featured topics include polygonal, pyramidal, and figurate numbers; linear diophantine equations and congruences; partitions; rational right triangles; triangles, quadrilaterals, and tetrahedra; the sums of two, three, four, and n squares; the number of solutions of quadratic congruences in n unknowns; Liouville's series of eighteen articles; the Pell equation; squares in arithmetical or geometrical progression; equations of degrees three, four, and n; sets of integers with equal sums of like powers; Waring's problem and related results; Fermat's last theorem; and many other related subjects. Indexes of authors cited and subjects appear at the end of the book. |
Autres éditions - Tout afficher
History of the Theory of Numbers, Volume II: Diophantine Analysis Leonard Eugene Dickson Aucun aperçu disponible - 2013 |
Expressions et termes fréquents
a₁ Acad Algebra Amer Archiv Math Arith biquadrates coefficients Comm Comptes Rendus Paris congruences continued fraction cubes Diophantus divided divisible divisors equal equation Euler expressed Fermat Fermat's last theorem formula French transl functions gave Genocchi given number gives Hence Heron triangle hypotenuse Ibid infinitude Jour L'intermédiaire des math linear Mém method multiply noted Nouv number of partitions number of representations obtained odd number odd prime Oeuvres papers Pell equation Phys positive integers positive integral solutions proof proved quadratic forms quadratic residue Quest quotient rational quadrilaterals rational triangles relatively prime result right triangle roots sets of solutions sides solvable solved Sphinx-Oedipe sum of three theorem three numbers three squares treated triangular numbers unity values whence