題組內容

There are 7 problems in this test. No calculators are allowed. Write down detailed steps for the solution to each problem. Otherwise, no credits for that problem will be given.

1. Let x1, x2, , be a sequence of n integers. A consecutive subsequence of x1,x2,... ., is a subsequence for some i, j, 1 ≤ i ≤ j ≤n. Show that for any k, I k n, there is a consecutive subsequence whose sum is divisible by k.

題組內容

1. Let x1, x2, , be a sequence of n integers. A consecutive subsequence of x1,x2,... ., is a subsequence for some i, j, 1 ≤ i ≤ j ≤n. Show that for any k, I k n, there is a consecutive subsequence whose sum is divisible by k.

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