I am trying to solve this problem. http://www.javaist.com/rosecode/problem-527-1-2-3-type-Pythagorean-triangles-askyear-2018
Here we have to find all positive integral solution of $a^2+2b^2=3c^2$ where $a+b+c\le N$. In the question, $N=25000000$.
My first approach was to loop over $a$ and for fixed value of $a$ find the solutions of $3c^2-2b^2=a^2$ using LMM algorithm (https://thilinaatsympy.wordpress.com/2013/07/06/solving-the-generalized-pell-equation/). But this is very slow. I am unable to find a faster method. Any help will be appreciated.