Find the number of ordered pairs!

\[ \large x^2 - px + q = 0 \qquad \qquad x^2-qx +p = 0 \]

Let \(p\) and \(q\) be positive integers such that the two quadratic equations above have unequal integer roots (in \(x\)).

Find the number of ordered solutions \((p,q) \) satisfying the above conditions.

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