SE-SKOLORNAS 1976 Problem 3

If $a$ , $b$ , $c$ are rational, show that $\frac{1}{(b-c)^2}+\frac{1}{(c-a)^2}+\frac{1}{(a-b)^2}$ is the square of a rational.

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.