I need to prove that the equation x^2 - 3y^2 = 1 has infinite solutions where x and y are both positive integers. I'm supposed to use the method of ascent.
As a hint, it says to solve this problem by showing how, given one solution (u, v), you can find another solution (w, z) that is larger. Then the proof will involve finding two formulas, like w = x + y and z = x - y. These formulas won't actually work, but there is a pair of second degree formulas which will work. One of them has a cross term and one involves the number 3.
The Attempt at a Solution
The problem is, I've never used the method of ascent before. I have used the method of descent to solve one problem, and I assume that it's like applying descent in reverse. I have no idea how to do this, however. Can I please get some help?