MathDB

Find all second degree polynomial

d(x)=x^{2}+ax+b

with integer coefficients, so that there exists an integer coefficient polynomial

p(x)

and a non-zero integer coefficient polynomial

q(x)

that satisfy: \left( p(x) \right)^{2}-d(x) \left( q(x) \right)^{2}=1, \forall x \in \mathbb R.

Problem Statement