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The uniformity conjecture postulates a relationship between the syntactic length of expressions built up from the natural numbers using field operations, exponentials, and ...

A pair of numbers m and n such that sigma^*(m)=sigma^*(n)=m+n, where sigma^*(n) is the unitary divisor function. Hagis (1971) and García (1987) give 82 such pairs. The first ...

A "visual representation" number which is a sum of some simple function of its digits. For example, 1233 = 12^2+33^2 (1) 2661653 = 1653^2-266^2 (2) 221859 = 22^3+18^3+59^3 ...

As defined by Gray (1997, p. 201), Viviani's curve, sometimes also called Viviani's window, is the space curve giving the intersection of the cylinder of radius a and center ...

The W-transform of a function f(x) is defined by the integral where Gamma[(beta_m)+s, 1-(alpha_n)-s; (alpha_p^(n+1))+s, 1-(beta_q^(m+1))-s] =Gamma[beta_1+s, ..., beta_m+s, ...

Find nontrivial solutions to sigma(x^2)=sigma(y^2) other than (x,y)=(4,5), where sigma(n) is the divisor function. Nontrivial solutions means that solutions which are ...

A weakly binary tree is a planted tree in which all nonroot graph vertices are adjacent to at most three graph vertices. Let g(z)=sum_(i=0)^inftyg_iz^i, (1) be the generating ...

A weighted adjacency matrix A_f of a simple graph is defined for a real positive symmetric function f(d_i,d_j) on the vertex degrees d_i of a graph as ...

A statistic w on the symmetric group S_n is called a weighted inversion statistic if there exists an upper triangular matrix W=(w_(ij)) such that ...

Let a piecewise smooth function f with only finitely many discontinuities (which are all jumps) be defined on [-pi,pi] with Fourier series a_k = 1/piint_(-pi)^pif(t)cos(kt)dt ...