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deleting rows and columns including perfect squares

Source: Middle European Mathematical Olympiad 2013 T-7

May 17, 2014
quadraticsceiling functionnumber theory proposednumber theory

Problem Statement

The numbers from 1 to 20132 2013^2 are written row by row into a table consisting of 2013×2013 2013 \times 2013 cells. Afterwards, all columns and all rows containing at least one of the perfect squares 1,4,9,⋯ ,20132 1, 4, 9, \cdots, 2013^2 are simultaneously deleted. How many cells remain?
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