Let α be the positive root of the equation x^2 \minus{} 1989x \minus{} 1 \equal{} 0. Prove that there exist infinitely many natural numbers n that satisfy the equation:
\lfloor \alpha n \plus{} 1989 \alpha \lfloor \alpha n \rfloor \rfloor \equal{} 1989n \plus{} \left( 1989^2 \plus{} 1 \right) \lfloor \alpha n \rfloor. floor functionpigeonhole principlealgebra unsolvedalgebra