Problem

Source: Moldova TST 2018

Tags: algebra, polynomial



Let $n, \in \mathbb {N^*} , n\ge 3$ a) Prove that the polynomial $f (x)=\frac {X^{2^n-1}-1}{X-1}-X^n $ has a divisor of form $X^p +1$ where $p\in\mathbb {N^*} $ b) Show that for $n=7$ the polynomial $f (X) $ has three divisors with integer coefficients .