Number Theory Level 4

All pairs $$(a. b)$$ of positive integers such that $$a{b}^{2} + b + 7$$ divides $${a}^{2}b+ a + b$$ are given by
$$(p, q)$$ ; $$(s, t)$$ and $$(\alpha, \beta)$$.

Find the value of $$p + q + s + t$$.

Here, $$\alpha, \beta$$ varies over a variable for example it can be $$(4{ a }^{ 2 }, 5a)$$ for some variable $$a$$.

And $$p, q, s, t$$ are natural numbers.

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