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A Ruth-Aaron pair is a pair of consecutive numbers (n,n+1) such that the sums of the prime factors of n and n+1 are equal. They are so named because they were inspired by the ...

The tribonacci numbers are a generalization of the Fibonacci numbers defined by T_1=1, T_2=1, T_3=2, and the recurrence equation T_n=T_(n-1)+T_(n-2)+T_(n-3) (1) for n>=4 ...

An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of ...

The arf invariant is a link invariant that always has the value 0 or 1. A knot has Arf invariant 0 if the knot is "pass equivalent" to the unknot and 1 if it is pass ...

Ball point picking is the selection of points randomly placed inside a ball. n random points can be picked in a unit ball in the Wolfram Language using the function ...

There are two definitions of the Carmichael function. One is the reduced totient function (also called the least universal exponent function), defined as the smallest integer ...

The common logarithm is the logarithm to base 10. The notation logx is used by physicists, engineers, and calculator keypads to denote the common logarithm. However, ...

A strongly regular graph with parameters (n,k,a,c) has graph eigenvalues k, theta, and tau, where theta = ((a-c)+sqrt(Delta))/2 (1) tau = ((a-c)-sqrt(Delta))/2 (2) where ...

A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). To examine the transformation properties of a contravariant tensor, ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...