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Number Theory: An Approach Through History from Hammurapi to Legendre is a book on the history of number theory, written by André Weil and published in 1984. [1]The book reviews over three millennia of research on numbers but the key focus is on mathematicians from the 17th century to the 19th, in particular, on the works of the mathematicians Fermat, Euler, Lagrange, and Legendre paved the ...
Basic Number Theory is an influential book [1] by André Weil, an exposition of algebraic number theory and class field theory with particular emphasis on valuation-theoretic methods. Based in part on a course taught at Princeton University in 1961–62, it appeared as Volume 144 in Springer's Grundlehren der mathematischen Wissenschaften ...
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
An Introduction to the Theory of Numbers is a classic textbook in the field of number theory, by G. H. Hardy and E. M. Wright. The book grew out of a series of lectures by Hardy and Wright and was first published in 1938. The third edition added an elementary proof of the prime number theorem, and the sixth edition added a chapter on elliptic ...
Its authors have divided Elementary Number Theory, Group Theory and Ramanujan Graphs into four chapters. The first of these provides background in graph theory, including material on the girth of graphs (the length of the shortest cycle), on graph coloring, and on the use of the probabilistic method to prove the existence of graphs for which both the girth and the number of colors needed are ...
Bernoulli number. Agoh–Giuga conjecture; Von Staudt–Clausen theorem; Dirichlet series; Euler product; Prime number theorem. Prime-counting function. Meissel–Lehmer algorithm; Offset logarithmic integral; Legendre's constant; Skewes' number; Bertrand's postulate. Proof of Bertrand's postulate; Proof that the sum of the reciprocals of the ...
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers , finite fields , and function fields .
Traditionally, number theory is the branch of mathematics concerned with the properties of integers and many of its open problems are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arise naturally from the study of integers.
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