A Pell-type equation in general may not have integer solutions (for example, the equation \(x^2-3y^2=2\)). When it does, it is possible to describe the general solution.

Consider the general equation \(N(z)=a\). Like in Theorem 1, one can show that all its solutions can be obtained from the solutions \(z\) with \(1\leq z\leq z_0\), where \(z_0\) is the smallest non-trivial solution of Pell’s equation \(N(z)=1\). Thus it is always sufficient to check finitely many values of \(x\). Moreover, there is a simple upper bound for those \(x\).