I'm stuck solving a diophantine equation. It's mostly because I don't know how to solve equations resembling Pell's equation.
I have to solve this equation with (x,y) in Z.
x^2 + 2x + 3 = 10 y^2 + 11y + 12
I reduce the problem, into this :
(20y+11)^2 - 40*(x+1)^2 + 279 = 0
Y^2 - 40X^2 + 279 =0 with Y = 20y+11 and X=x+1
From that moment on, I don't know how to go on. Already, there is a condition where Y = 11 mod 20 and moreover I don't know how to solve it with Pell's equation.
Thanks for the help !