Problem 2. For a positive integer k, call an integer a pure k-th power if it can be represented as m^k for some integer m. Show that for every positive integer n there exist n distinct positive integers such that their sum is a pure 2009-th power, and their product is a pure 2010-th power. Set a1,...,an distinct. N = a1^2010 + a2^2010 + ... + an^2010 Define Xi = N^(2010*2008) ai^2010 Then X1+X2+...+Xn = N^(2010*2008) * N = (N^2009)^2009, a pure 2009-th power X1X2...Xn = (N^2008n a1a2...an) ^ 2010, a pure 2010-th power... 好像太簡單了... -- r=e^theta 即使有改變，我始終如一。 --

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