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An integer n is p-balanced for p a prime if, among all nonzero binomial coefficients (n; k) for k=0, ..., n (mod p), there are equal numbers of quadratic residues and ...

Let m>=3 be an integer and let f(x)=sum_(k=0)^na_kx^(n-k) be an integer polynomial that has at least one real root. Then f(x) has infinitely many prime divisors that are not ...

In the American system, one billion equals 10^9=1000000000. In the French and German systems, one billion equals 10^(12). In recent years, the "American" system has become ...

The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic ...

An odd prime p is called a cluster prime if every even positive integer less than p-2 can be written as a difference of two primes q-q^', where q,q^'<=p. The first 23 odd ...

Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...

A cusp form is a modular form for which the coefficient c(0)=0 in the Fourier series f(tau)=sum_(n=0)^inftyc(n)e^(2piintau) (1) (Apostol 1997, p. 114). The only entire cusp ...

The term diamond is another word for a rhombus. The term is also used to denote a square tilted at a 45 degrees angle. The diamond shape is a special case of the superellipse ...

The dominance relation on a set of points in Euclidean n-space is the intersection of the n coordinate-wise orderings. A point p dominates a point q provided that every ...

There are infinitely many primes m which divide some value of the partition function P.