MathDB

10

Part of 1985 ITAMO

Problems(1)

A representation using floor

Source:

3/14/2006
How many of the first 1000 positive integers can be expressed in the form ⌊2x⌋+⌊4x⌋+⌊6x⌋+⌊8x⌋, \lfloor 2x \rfloor + \lfloor 4x \rfloor + \lfloor 6x \rfloor + \lfloor 8x \rfloor, where xx is a real number, and ⌊z⌋\lfloor z \rfloor denotes the greatest integer less than or equal to zz?
floor functioncalculusintegrationfunction