IrMO 1990 Problem 4

The real number $x$ satisfies all the inequalities $2^k<x^k+x^{k+1}<2^{k+1}$ for $k=1,2,\dots ,n$ . What is the greatest possible value of $n$ ?

Dataset text AI-MO AoPS. 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.