When a Pell's equation is solvable, then the solution with the smallest $x$ is called this equation's fundamental solution. All other solutions can be derived by the fundamental solution by a well-known formula. Therefore, to solve a Pell's solution is to find its fundamental solution.

As a Pell's solution is uniquely determined by the coefficient $d$, it is possible to create a table listing all the fundamental solutions corresponding to every possible value of $d$. This is called the table of fundamental solutions.

Please refer to the attachment for the table of fundamental solutions and the general solution formulas.