PL-OM 1998 Problem 1

Prove that among the numbers of the form $50^n + (50n+1)^{50}$ , where $n$ is a natural number, there exist infinitely many composite numbers.

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.