KöMaL 2017 B4845

Prove that each term of the sequence $a_1 =1,$ $a_n =\frac{4a_{n-1}+\sqrt{7a^2_{n-1}-3}}{3}; n\ge2$ is rational.

Official text KöMaL. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.