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A primitive root of a prime p is an integer g such that g (mod p) has multiplicative order p-1 (Ribenboim 1996, p. 22). More generally, if GCD(g,n)=1 (g and n are relatively ...

Calculating the 13th root of a large number (that is a perfect 13th power) is a famous mental calculation challenge. However, because of difficulties in standardizing the ...

Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

The square root method is an algorithm which solves the matrix equation Au=g (1) for u, with A a p×p symmetric matrix and g a given vector. Convert A to a triangular matrix ...

The square root inequality states that 2sqrt(n+1)-2sqrt(n)<1/(sqrt(n))<2sqrt(n)-2sqrt(n-1) for n>=1.

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9. The concept ...

Let sum_(k=1)^(infty)u_k be a series with positive terms, and let rho=lim_(k->infty)u_k^(1/k). 1. If rho<1, the series converges. 2. If rho>1 or rho=infty, the series ...

A special graph vertex that is designated to turn a tree into a rooted tree or a graph into a rooted graph. The root is sometimes also called "eve," or an "endpoint" (Saaty ...

Consider the process of taking a number, taking its digit sum, then adding the digits of numbers derived from it, etc., until the remaining number has only one digit. The ...