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[x] denotes the greatest integer not exceeding x

Source: China south east mathematical Olympiad 2007 problem 3

July 12, 2013
functionnumber theory unsolvednumber theory

Problem Statement

Let ai=min{k+ik∣k∈N∗}a_i=min\{ k+\dfrac{i}{k}|k \in N^*\}, determine the value of Sn2=[a1]+[a2]+⋯+[an2]S_{n^2}=[a_1]+[a_2]+\cdots +[a_{n^2}], where n≥2n\ge 2 . ([x][x] denotes the greatest integer not exceeding x)
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