Binomial number

In mathematics, specifically in number theory, a binomial number is an integer which can be obtained by evaluating a homogeneous polynomial containing two terms. It is a generalization of a Cunningham 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 ${\displaystyle \scriptstyle x^{n}\,\pm \,y^{n}}$, with ${\displaystyle \scriptstyle x\,>\,y}$ and ${\displaystyle \scriptstyle n\,>\,1}$. However, since ${\displaystyle \scriptstyle x^{n}\,-\,y^{n}}$ is always divisible by ${\displaystyle \scriptstyle x\,-\,y}$, when studying the numbers generated from the version with the negative sign, they are usually divided by ${\displaystyle \scriptstyle x\,-\,y}$ first. Binomial numbers formed this way form Lucas sequences. Specifically:

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