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Let p be an odd prime, a be a positive number such that pa (i.e., p does not divide a), and let x be one of the numbers 1, 2, 3, ..., p-1. Then there is a unique x^', called ...

The number of ways in which a group of n with weights sum_(i=1)^(n)w_i=1 can change a losing coalition (one with sumw_i<1/2) to a winning one, or vice versa. It was proposed ...

If a sequence takes only a small number of different values, then by regarding the values as the elements of a finite field, the Berlekamp-Massey algorithm is an efficient ...

Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region ...

There are two identities known as Catalan's identity. The first is F_n^2-F_(n+r)F_(n-r)=(-1)^(n-r)F_r^2, where F_n is a Fibonacci number. Letting r=1 gives Cassini's ...

A random number generator produced by iterating X_(n+1)=|100lnX_n (mod 1)| for a seed X_0=0.1. This simple generator passes the noise sphere test for randomness by showing no ...

A clique covering of a graph G is set of cliques such that every vertex of G is a member of at least one clique. A minimum clique covering is a clique covering of minimum ...

In 1976, Coates and Wiles showed that elliptic curves with complex multiplication having an infinite number of solutions have L-functions which are zero at the relevant fixed ...

Complex infinity is an infinite number in the complex plane whose complex argument is unknown or undefined. Complex infinity may be returned by the Wolfram Language, where it ...

A complex magnification is a map of the form z|->az, where a is a positive real number, which corresponds to magnification about the origin of points in the complex plane by ...