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The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

A plane partition is a two-dimensional array of integers n_(i,j) that are nonincreasing both from left to right and top to bottom and that add up to a given number n. In ...

The constant pi, denoted pi, is a real number defined as the ratio of a circle's circumference C to its diameter d=2r, pi = C/d (1) = C/(2r) (2) pi has decimal expansion ...

A (v,g)-cage graph is a v-regular graph of girth g having the minimum possible number of nodes. When v is not explicitly stated, the term "g-cage" generally refers to a ...

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...

Legendre showed that there is no rational algebraic function which always gives primes. In 1752, Goldbach showed that no polynomial with integer coefficients can give a prime ...

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

Twin primes are pairs of primes of the form (p, p+2). The term "twin prime" was coined by Paul Stäckel (1862-1919; Tietze 1965, p. 19). The first few twin primes are n+/-1 ...

An interval into which a given data point does or does not fall.

Solve the Pell equation x^2-92y^2=1 in integers. The smallest solution is x=1151, y=120.