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

\[ f(x_1, y_1) \neq f(x_2, y_2 ) ?\]

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