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The first of the Hardy-Littlewood conjectures. The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

Find a square number x^2 such that, when a given integer h is added or subtracted, new square numbers are obtained so that x^2+h=a^2 (1) and x^2-h=b^2. (2) This problem was ...

A field is any set of elements that satisfies the field axioms for both addition and multiplication and is a commutative division algebra. An archaic name for a field is ...

A divisor d of n for which GCD(d,n/d)=1, (1) where GCD(m,n) is the greatest common divisor. For example, the divisors of 12 are {1,2,3,4,6,12}, so the unitary divisors are ...

The term "Euler function" may be used to refer to any of several functions in number theory and the theory of special functions, including 1. the totient function phi(n), ...

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...

The proposal originally made by Georg Cantor that there is no infinite set with a cardinal number between that of the "small" infinite set of integers aleph_0 and the "large" ...

A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The first is the idea ...

The chromatic number of a graph G is the smallest number of colors needed to color the vertices of G so that no two adjacent vertices share the same color (Skiena 1990, p. ...