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A positive even value of n for which phi(x)=n, where phi(x) is the totient function, has no solution. The first few are 14, 26, 34, 38, 50, ... (OEIS A005277).

A quantity which does not equal zero is said to be nonzero. A real nonzero number must be either positive or negative, and a complex nonzero number can have either real or ...

An impartial game in which the last player wins. In normal-form games, the nim-value of the sum of two games is the nim-sum of their nim-values.

The normal bundle of a submanifold N in M is the vector bundle over N that consists of all pairs (x,v), where x is in N and v is a vector in the vector quotient space ...

Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is ...

Given a matrix equation Ax=b, the normal equation is that which minimizes the sum of the square differences between the left and right sides: A^(T)Ax=A^(T)b. It is called a ...

A normal extension is the splitting field for a collection of polynomials. In the case of a finite algebraic extension, only one polynomial is necessary.

Let G be a group with normal series (A_0, A_1, ..., A_r). A normal factor of G is a quotient group A_(k+1)/A_k for some index k<r. G is a solvable group iff all normal ...

A line along a normal vector (i.e., perpendicular to some tangent line). If K subset R^d is a centrosymmetric set which has a twice differentiable boundary, then there are ...

In every residue class modulo p, there is exactly one integer polynomial with coefficients >=0 and <=p-1. This polynomial is called the normal polynomial modulo p in the ...