IT-CESENATICO 2004 Problem 3

(a) Is $2005^{2004}$ the sum of two perfect squares? (b) Is $2004^{2005}$ the sum of two perfect squares?

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.