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Any composite number n with p|(n/p-1) for all prime divisors p of n. n is a Giuga number iff sum_(k=1)^(n-1)k^(phi(n))=-1 (mod n) (1) where phi is the totient function and ...

The first Hardy-Littlewood conjecture is called the k-tuple conjecture. It states that the asymptotic number of prime constellations can be computed explicitly. A particular ...

An elliptic partial differential equation given by del ^2psi+k^2psi=0, (1) where psi is a scalar function and del ^2 is the scalar Laplacian, or del ^2F+k^2F=0, (2) where F ...

The incentral circle is the circumcircle of the incentral triangle. It has radius R_I=(sqrt(abcf(a,b,c)f(b,c,a)f(c,a,b)))/(8Delta(a+b)(a+c)(b+c)), (1) where Delta is the area ...

The inner Vecten circle is the circumcircle of the inner Vecten triangle. It has center at Kimberling center X_(642), which is the complement of the inner Vecten point ...

The Kähler potential is a real-valued function f on a Kähler manifold for which the Kähler form omega can be written as omega=ipartialpartial^_f. Here, the operators ...

A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...

A goodness-of-fit test for any statistical distribution. The test relies on the fact that the value of the sample cumulative density function is asymptotically normally ...

Landau's function g(n) is the maximum order of an element in the symmetric group S_n. The value g(n) is given by the largest least common multiple of all partitions of the ...

The spherical harmonics form a complete orthogonal system, so an arbitrary real function f(theta,phi) can be expanded in terms of complex spherical harmonics by ...