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The number-theorist Leonard Dickson (1874–1954) said "Thank God that number theory is unsullied by any application". Such a view is no longer applicable to number theory. [ 88 ] In 1974, Donald Knuth said "virtually every theorem in elementary number theory arises in a natural, motivated way in connection with the problem of making computers ...
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 ...
Composite number. Highly composite number; Even and odd numbers. Parity; Divisor, aliquot part. Greatest common divisor; Least common multiple; Euclidean algorithm; Coprime; Euclid's lemma; Bézout's identity, Bézout's lemma; Extended Euclidean algorithm; Table of divisors; Prime number, prime power. Bonse's inequality; Prime factor. Table of ...
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.
Vorlesungen über Zahlentheorie (German pronunciation: [ˈfoːɐ̯ˌleːzʊŋən ˈyːbɐ ˈtsaːlənteoˌʁiː]; German for Lectures on Number Theory) is the name of several different textbooks of number theory. The best known was written by Peter Gustav Lejeune Dirichlet and Richard Dedekind, and published in 1863.
Expander graphs have many applications to computer science, number theory, and group theory, see e.g Lubotzky's survey on applications to pure and applied math and Hoory, Linial, and Wigderson's survey which focuses on computer science. Ramanujan graphs are in some sense the best expanders, and so they are especially useful in applications ...
Rudin's conjecture is a mathematical conjecture in additive combinatorics and elementary number theory about an upper bound for the number of squares in finite arithmetic progressions. The conjecture, which has applications in the theory of trigonometric series, was first stated by Walter Rudin in his 1960 paper Trigonometric series with gaps ...
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 ...