On the factorization of $x^{d_r}+x^{d_{r-1}}+\cdots +x^{d_2}+x^{d_1}+p$ and a conjecture of C. Nicol

Michael Filaseta, Lilit Martirosyan, London Cameron Swan

For an arbitrary prime $p$ and arbitrary positive integers $r$ and $d_1,\dots ,d_r$ with $d_r>\cdots >d_1$, we show that $x^{d_{r}} + x^{d_{r-1}} + \cdots + x^{d_{2}}…