# Lucky number 9!

For every integer $$0 \leq i \leq 9$$ and $$a_i \in (0,1,2,3,4)$$, given that $$\displaystyle 6\sum_{i=0}^{9} a_i 5^i$$ $$\equiv$$ $$1$$ $$mod$$ $$(5^{10})$$.

Find the value of $$a_{9}$$.

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