# A Modular Recursion Sequence?

Number Theory Level 4

Let recursion $$a_i$$ be defined as:

$$a_n=a_{n-1}+a_{n-2} \pmod{10}$$

where all terms in the sequence are positive integers less than ten. For any given $$a_1$$ and $$a_2$$, a distinct sequence is formed. For example, if $$a_1=5$$ and $$a_2=4$$, the sequence would go 5, 4, 9, 3, 2, 5, 7, 2, 9, 1, so on and so forth. If $$a_6=6$$, find the sum of all possible values of $$a_1$$.

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