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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."
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
The German edition includes all of his papers on number theory: all the proofs of quadratic reciprocity, the determination of the sign of the Gauss sum, the investigations into biquadratic reciprocity, and unpublished notes. Gauss, Carl Friedrich; Clarke, Arthur A. (1986), Disquisitiones Arithemeticae (2nd corrected ed.),
James Victor Uspensky (Russian: Яков Викторович Успенский, romanized: Yakov Viktorovich Uspensky; April 29, 1883 – January 27, 1947) was a Russian and American mathematician notable for writing Theory of Equations. [2] [3]
Download as PDF; Printable version; From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Number theory#Elementary number theory; Retrieved from " ...
Many mathematicians then attempted to construct elementary proofs of the theorem, without success. G. H. Hardy expressed strong reservations; he considered that the essential "depth" of the result ruled out elementary proofs: No elementary proof of the prime number theorem is known, and one may ask whether it is reasonable to expect one.
In number theory, Bonse's inequality, named after H. Bonse, [1] relates the size of a primorial to the smallest prime that does not appear in its prime factorization.It states that if p 1, ..., p n, p n+1 are the smallest n + 1 prime numbers and n ≥ 4, then