IZhO 2021 Problem 1

Prove that there exists a positive integer $n$ , such that the remainder of $3^n$ when divided by $2^n$ is greater than $10^{2021}$ .

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.