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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 ...
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 elementary number is one formalization of the concept of a closed-form number. The elementary numbers form an algebraically closed field containing the roots of arbitrary expressions using field operations, exponentiation, and logarithms. The set of the elementary numbers is subdivided into the explicit elementary numbers and the implicit ...
Download as PDF; Printable version; From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Number theory#Elementary number theory; Retrieved from " ...
Download as PDF; Printable version; In other projects ... Square-free. Square-free integer ... Computational number theory is also known as algorithmic number theory ...
Download as PDF; Printable version; ... 1947) was a Russian and American mathematician notable for writing Theory of Equations. ... Elementary Number Theory. Uspensky ...
Many other theorems in elementary number theory, such as Euclid's lemma or the Chinese remainder theorem, result from Bézout's identity. A Bézout domain is an integral domain in which Bézout's identity holds. In particular, Bézout's identity holds in principal ideal domains. Every theorem that results from Bézout's identity is thus true in ...
Elementary number theory includes topics of number theory commonly taught at the primary and secondary school level, or in college courses on introductory number theory. Shortcut {{ MSC }}