A note on some properties of the $\lambda$-Polynomial

The expression $a^n+b^n$ can be factored as $(a+b)(a^{n-1} - a^{n-2} b + a^{n-3} b^2 - … + b^{n-1})$when$n$ is an odd integer greater than one. This paper focuses on proving a few properties of the longer factor above, which we call ${\lambda }_n(a,b)$. One such property is that the primes which divide ${\lambda }_n(a,b)$ satsify $p\ge n$, if $a,b$ are coprime integers and $n$ is an odd prime.