ISL 1979 Problem 18

Show that for no integers $a \geq 1, n \geq 1$ is the sum $1+\frac{1}{1+a}+\frac{1}{1+2a}+\cdots+\frac{1}{1+na}$ an integer.

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.