# one of the best

Algebra Level 5

Let,

$$\large S_n = a_1^n + a_2^n + a_3^n + a_4^n + a_5^n + a_6^n + a_7^n + a_8^n + a_9^n + a_{10}^n + a_{11}^n + a_{12}^n$$

Given that,

$$\large S_1 = S_2 = S_3 = S_4 = S_6 = S_8 = S_9 = S_{11} = 0$$

$$\large S_5 = 35$$ , $$\large S_7 = 14$$ , $$\large S_{10} = 245$$ , $$\large S_{12} = 168$$

Find the largest value of $$n$$ for which $$\large S_n = 0$$

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