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Question: a_1+a_2+...+a_n | a_1^i+a_2^i+...+a_n^i

Source: Iran TST 2006

April 30, 2006
algebrapolynomialnumber theorydivisibility testsnumber theory proposed

Problem Statement

Let nn be a fixed natural number. Find all nn tuples of natural pairwise distinct and coprime numbers like a1,a2,…,ana_1,a_2,\ldots,a_n such that for 1≤i≤n1\leq i\leq n we have a1+a2+…+an∣a1i+a2i+…+ani a_1+a_2+\ldots+a_n|a_1^i+a_2^i+\ldots+a_n^i
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