# Exponential divisibility?

Number Theory Level 5

Let the $$n$$ ordered pairs $$(a,b)$$ such that $$7^a-3^b$$ divides $$a^4+b^2$$ and $$a,b\in N$$ be $$(a_{1},b_{1}),(a_{2},b_{2}),...,(a_{n},b_{n})$$. Calculate $$\displaystyle\sum_{i=1}^{n} (a_{i}+b_{i})$$

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