MathDB
A representation using floor

Source:

March 14, 2006
floor functioncalculusintegrationfunction

Problem Statement

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?