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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 ...

The Chebyshev polynomials of the first kind are a set of orthogonal polynomials defined as the solutions to the Chebyshev differential equation and denoted T_n(x). They are ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

The Wiener sum index WS is a graph index defined for a graph on n nodes by WS=1/2sum_(i=1)^nsum_(j=1)^n((d)_(ij))/((Omega)_(ij)), where (d)_(ij) is the graph distance matrix ...

A prime p for which 1/p has a maximal period decimal expansion of p-1 digits. Full reptend primes are sometimes also called long primes (Conway and Guy 1996, pp. 157-163 and ...

Hardy and Littlewood (1914) proved that the sequence {frac(x^n)}, where frac(x) is the fractional part, is equidistributed for almost all real numbers x>1 (i.e., the ...

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 ...

An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0+kd}_(k=0)^(n-1) such that the differences between successive terms is a ...