If [x] denotes the greatest positive integer less than or equal x , then evaluate: x - [x] = (x - [x])2011

x - [x] = fractional part of x so the equation reduces to {x} = {x}^2011 .. where {x} denotes fractional part of x.. so fraction power a large valure is =0 so rhs becomes close to zero and lhs is non zero so for the equality to hold.. {x} must be =0 meaning x is an integer .. so set of all integers satisfy the above equation ... approve my answer if you have understood the solution