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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 ...

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 ...

A real normed algebra, also called a composition algebra, is a multiplication * on R^n that respects the length of vectors, i.e., |x*y|=|x|*|y| for x,y in R^n. The only real ...

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 ...

A real function is said to be analytic if it possesses derivatives of all orders and agrees with its Taylor series in a neighborhood of every point.

Pathological functions that are continuous but differentiable only on a set of points of measure zero are sometimes known as monsters of real analysis. Examples include the ...