# Unique Percentage

Number Theory Level pending

Let $$x <y$$ be positive integers such that $$\gcd(x,y)=1$$. We define

$f(x,y) = \dfrac{\left\lfloor \dfrac{x}{y} \times 100 \right\rfloor}{100}$

What is the greatest integer $$G$$, such that for any $$x_1,x_2, y_1,y_2 \leq G$$ satisfying $$x_1 \neq x_2, y_1 \neq y_2$$, we have

$f(x_1, y_1) \neq f(x_2, y_2 ) ?$

×