3i tried this. [nx] - [x] = 1. for n = 1, there is no solution. for n = 2, the soultions are - [1/2 , 3/2). for n = 3, the solutions are - [1/3, 2/3). for n = 4, the solutions are - [1/4, 2/4). so generalising it, for any n > 2 the solutions are - [1/n, 2/n). but i am not sure of other solutions. so i have put this Q on aops.
i editted the part for n = 2. that was wrong.
i had done [1/2 , 1). the aops solution says that i am correct.
:)
