Solving The Fermat-Pell’s Equation with Infinite Continuous Fractions - Suyudi, Mochamad (International Journal of Global Operations Research, 2022)
The special form is called the Fermat-Pell’s equation where is a positive integer that is not a square. Let's say the solution of this equation is a positive solution as long as x and y are both positive. Since solutions beyond can be arranged in sets of four by sign combinations , it is clear that all solutions will be known once all positive solutions are found. The result which gives us a starting point confirms that any pair of positive integers satisfying the Fermat-Pell’s equation can be obtained from infinite continuous fraction denoting the irrational number √ .