KöMaL 2011 A545

Prove that whenever $a$ > $b$ >1 are integers such that $a$ + $b$ divides $ab$ +1 and $a$ - $b$ divides $ab$ -1 then $a<b\sqrt3$ .

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.