# EGMO 2012

Let $$(a_1,b_1)$$, $$(a_2,b_2)$$, $$...$$, $$(a_n,b_n)$$ be all the pairs of prime numbers that satisfy $\frac{a}{a+1}+\frac{b+1}{b}=\frac{2n}{n+2}$ for some positive integer $$n$$. Then find the sum of all possible values of $$b-a$$.

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