Search Results for ""

The two-argument Ramanujan function is defined by phi(a,n) = 1+2sum_(k=1)^(n)1/((ak)^3-ak) (1) = 1-1/a(H_(-1/a)+H_(1/a)+2H_n-H_(n-1/a)-H_(n+1/a)). (2) The one-argument ...

Informally, a function f is a one-way function if 1. The description of f is publicly known and does not require any secret information for its operation. 2. Given x, it is ...

Attractive compounds of four octahedra can be constructed as the duals of the cube 4-compounds. These compounds will be implemented in a future version of the Wolfram ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...

The absolute value of a real number x is denoted |x| and defined as the "unsigned" portion of x, |x| = xsgn(x) (1) = {-x for x<=0; x for x>=0, (2) where sgn(x) is the sign ...

In an additive group G, the additive inverse of an element a is the element a^' such that a+a^'=a^'+a=0, where 0 is the additive identity of G. Usually, the additive inverse ...

A formula satisfied by all Hamiltonian cycles with n nodes. Let f_j be the number of regions inside the circuit with j sides, and let g_j be the number of regions outside the ...

In any tree, the number of dissimilar points minus the number of dissimilar lines plus the number of symmetry lines equals 1.

The largest cube dividing a positive integer n. For n=1, 2, ..., the first few are 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, ... (OEIS A008834).

Regardless of where one white and one black square are deleted from an ordinary 8×8 chessboard, the reduced board can always be covered exactly with 31 dominoes (of dimension ...