Binomial Number

A Binomial number is an integer obtained by evaluating a homogeneous polynomial containing two terms, also called a binomial. The form of this binomial is, with and . However, since is always divisible by, when studying the numbers generated from the version with the negative sign, they are usually divided by first. Binomial numbers formed this way form Lucas sequences. Specifically:

and

Binomial numbers are a generalization of a Cunningham numbers, and it will be seen that the Cunningham numbers are Binomial numbers where . Other subsets of the Binomial numbers are the Mersenne numbers and the Repunits.