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

Abstract

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.