On a polynomial involving roots of unity and its applications
On a polynomial involving roots of unity and its applications
Let [Formula: see text] be a prime. Gauss first introduced the polynomial [Formula: see text] where [Formula: see text] and [Formula: see text] varies over all quadratic residues modulo p and [Formula: see text]. Later Dirichlet investigated this polynomial and used this to solve problems involving the Pell equations. Recently, …