# Number-Theoretic Inequality!

**Number Theory**Level 5

\[\Large{0 < \left| \dfrac{p}{q} - \dfrac23 \right| < \dfrac{1}{q^2}}\]

How many ordered pairs \((p,q)\) of integers exists such that the above inequality satisfies?

\[\Large{0 < \left| \dfrac{p}{q} - \dfrac23 \right| < \dfrac{1}{q^2}}\]

How many ordered pairs \((p,q)\) of integers exists such that the above inequality satisfies?

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