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Difference of Floors

Source: 2003 IrMO Paper 1 Problem 3

December 28, 2017
algebra

Problem Statement

For each positive integer kk, let aka_k be the greatest integer not exceeding k\sqrt{k} and let bkb_k be the greatest integer not exceeding k3\sqrt[3]{k}. Calculate ∑k=12003(ak−bk).\sum_{k=1}^{2003} (a_k-b_k).
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