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A friendly number is a number that is a member of a friendly pair or a higher-order friendly n-tuple. Numbers that are not friendly are said to be solitary. There are some ...

Let f(x) be a monic polynomial of degree d with discriminant Delta. Then an odd integer n with (n,f(0)Delta)=1 is called a Frobenius pseudoprime with respect to f(x) if it ...

Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...

As defined by Erdélyi et al. (1981, p. 20), the G-function is given by G(z)=psi_0(1/2+1/2z)-psi_0(1/2z), (1) where psi_0(z) is the digamma function. Integral representations ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

Gaussian brackets are notation published by Gauss in Disquisitiones Arithmeticae and defined by [ ]=1 (1) [a_1]=a_1 (2) [a_1,a_2]=[a_1]a_2+[ ] (3) ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...

This is sometimes knows as the "bars and stars" method. Suppose a recipe called for 5 pinches of spice, out of 9 spices. Each possibility is an arrangement of 5 spices ...

Let p>3 be a prime number, then 4(x^p-y^p)/(x-y)=R^2(x,y)-(-1)^((p-1)/2)pS^2(x,y), where R(x,y) and S(x,y) are homogeneous polynomials in x and y with integer coefficients. ...

Let I(x,y) denote the set of all vertices lying on an (x,y)-graph geodesic in G, then a set S with I(S)=V(G) is called a geodetic set in G and is denoted g(G).