Invent a multiplication rule for solutions to x2 3y2 1 Tha

Invent a \"multiplication rule\" for solutions to x² - 3y² = 1. That is, if (x,y) and (u,v) are solutions, find a formula for producing a new solution, analogous to what we did in Section 5.2. Prove that your formula is correct.

*Section 5.2 can be found in Elements of Number Theory by John Stillwell*

Solution

x2-3y2=1 the multiplication rule for these solution

(x,y) (u,v) are producing a new solution.to determine the probability of intersection of several events