Diophantine Approximation on Quadratic Polynomials

48 Views Asked by At

Given an integer $a$ which is not a perfect square, I'd like to ask how to perform Diophantine Approximation of $\frac{x^2}{y^2}$ to $a$ where $x$ and $y$ are integers. Specifically, integers satisfying $|\frac{x^2}{y^2}-a|<\epsilon$ are preferred.