The value of each term of a sequence a1, a2, . . . , a2k is a positive integer and 2k X

Chapter 8, Problem 32

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The value of each term of a sequence a1, a2, . . . , a2k is a positive integer and 2k X i = 1 ai = 3k. Show that for each positive integer m k, there exist integers r and s with 1 r < s 2k such that s X i=r+1 ai = m. [Hint: Consider the cases when m < k and m = k separately.]

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