AUSTRIAN-POLISH 1990 Problem 2

Find all solutions in positive integers to $a^A = b^B = c^C = 1990^{1990}abc$ , where $A = b^c, B = c^a, C = a^b$ .

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.