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Find n

Source: China TST 2004 Quiz

February 1, 2009
algebra unsolvedalgebra

Problem Statement

Find all positive integer n n satisfying the following condition: There exist positive integers m m, a1 a_1, a2 a_2, ⋯ \cdots, a_{m\minus{}1}, such that \displaystyle n \equal{} \sum_{i\equal{}1}^{m\minus{}1} a_i(m\minus{}a_i), where a1 a_1, a2 a_2, ⋯ \cdots, a_{m\minus{}1} may not distinct and 1 \leq a_i \leq m\minus{}1.
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