Problem #3
Largest Number
Find the positive integer n less than 100000 for which the equation x^{2} = ny^{2} + 1 has the largest fundamental value of x. The fundamental value of (x, y) is the smallest positive non-trivial integral solution to the equation. (1,0) is the trivial solution.
Note: You can ignore those values of n for which there are no fundamental solution to the given equation.