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The sequence \{ a_n \} _ { n \ge 0 } is defined by a_0 = 2 , a_1 = 4 and
a_{n+1} = \frac{a_n a_{n-1}}{2} + a_n + a_{n-1}
for all positive integers n. Determine all prime numbers p for which there exists a positive integer m such that p divides the number a_m - 1.

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