7

Part of 2013 Middle European Mathematical Olympiad

Problems(1)

deleting rows and columns including perfect squares

Source: Middle European Mathematical Olympiad 2013 T-7

The numbers from 1 to

2013^2

are written row by row into a table consisting of

2013 \times 2013

cells. Afterwards, all columns and all rows containing at least one of the perfect squares

1, 4, 9, \cdots, 2013^2

are simultaneously deleted. How many cells remain?

quadraticsceiling functionnumber theory proposednumber theory