Find all real $\alpha$ s.t. \[ [ \sqrt{n + \alpha} + \sqrt{n} ] = [ \sqrt{4n+1} ] \] holds for all natural numbers $n$
Source: Indian Postal Coaching 2005
Tags: algebra unsolved, algebra
Find all real $\alpha$ s.t. \[ [ \sqrt{n + \alpha} + \sqrt{n} ] = [ \sqrt{4n+1} ] \] holds for all natural numbers $n$