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Consider separately when $N = 1^n + 8^n - 3^n - 6^n$ is divisible by $2$ and when it is divisible by $3$.
Obviously?
Age 14 to 18
Challenge Level 
Consider separately when $N = 1^n + 8^n - 3^n - 6^n$ is divisible by $2$ and when it is divisible by $3$.
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