# Divisibility Principles?

$\large{ S = \dfrac{(7^p - 2^p)(7^q - 2^q)}{pq} }$

Find all ordered pairs of primes $$(p,q)$$ where $$p \leq q$$, such that $$S$$ is an integer.

If the set of all such primes are $$\{ (p_1, q_1) \ , \ (p_2, q_2) \ ,\ \ldots \ , \ (p_n, q_n) \}$$, then find the value of:

$\large{\sum_{i=1}^n (p_i + q_i) = \ ? }$

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