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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 ...
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.
In elementary number theory, the lifting-the-exponent lemma (LTE lemma) provides several formulas for computing the p-adic valuation of special forms of integers. The lemma is named as such because it describes the steps necessary to "lift" the exponent of in such expressions.
Alonzo Church, "An unsolvable problem of elementary number theory", American Journal of Mathematics, 58 (1936), pp 345–363; Alonzo Church, "A note on the Entscheidungsproblem", Journal of Symbolic Logic, 1 (1936), pp 40–41. Davis, Martin (2001). Engines of logic: mathematicians and the origin of the computer. Norton paperback (1. publ. as ...
Composite number. Highly composite number; Even and odd numbers. Parity; Divisor, aliquot part. Greatest common divisor; Least common multiple; Euclidean algorithm; Coprime
Retrieved from "https://en.wikipedia.org/w/index.php?title=Elementary_number_theory&oldid=1216725872"https://en.wikipedia.org/w/index.php?title=Elementary_number_theory
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