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Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

Given two randomly chosen n×n integer matrices, what is the probability D(n) that the corresponding determinants are relatively prime? Hafner et al. (1993) showed that ...

Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

To solve the system of differential equations (dx)/(dt)=Ax(t)+p(t), (1) where A is a matrix and x and p are vectors, first consider the homogeneous case with p=0. The ...

If a is (directly) proportional to b, then a/b is a constant. The relationship is written a proportional b, which implies a=cb, for some constant c known as the constant of ...

If a polynomial P(x) is divided by (x-r), then the remainder is a constant given by P(r).

d_n=p_(n+1)-p_n. (1) The first few values are 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, ... (OEIS A001223). Rankin has shown that d_n>(clnnlnlnnlnlnlnlnn)/((lnlnlnn)^2) ...

Let f:M->N be a geodesic mapping. If either M or N has constant curvature, then both surfaces have constant curvature (Ambartzumian 1982, p. 26; Kreyszig 1991).

A spectrum containing the real numbers larger than Freiman's constant.

A zero function is a function that is almost everywhere zero. The function sometimes known as "the zero function" is the constant function with constant c=0, i.e., f(x)=0 ...