Find the remainder

Number Theory Level pending

Let n 1 n_1 , n 2 n_2 , n 3 n_3 , \ldots be the increasing sequence of natural numbers each of which leaves remainder r r when it is divided by r + 1 r+1 for r = 2 , 3 , 4 , , 9 r = 2,3,4,\ldots,9 . What is the remainder when n 2008 n_{2008} is divided by 11?


The answer is 5.

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