# 2010-4 Power and gcd

Let n, k be positive integers. Prove that $latex \sum_{i=1}^n k^{\gcd(i,n)}$ is divisible by n.

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# 2009-17 Relatively prime sequence

Let 1≤a1<a2<…<ak<n be a sequence of integers such that gcd(ai,aj)=1 for all 1≤i<j≤k. What is the maximum value of k?

(Problem updated on Sep. 26, 8AM: gcd(ai,aj)=1.)

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