# 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 \(a_1\).