MathDB
Polynomial problem

Source: Moldova TST 2018

April 6, 2018
algebrapolynomial

Problem Statement

Let n,∈N∗,n≥3n, \in \mathbb {N^*} , n\ge 3 a) Prove that the polynomial f(x)=X2n−1−1X−1−Xnf (x)=\frac {X^{2^n-1}-1}{X-1}-X^n has a divisor of form Xp+1X^p +1 where p∈N∗p\in\mathbb {N^*}
b) Show that for n=7n=7 the polynomial f(X)f (X) has three divisors with integer coefficients .
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