RO-NMO 2004 Problem 82

Prove that the equation $x^2+y^2+z^2+t^2=2^{2004}$ , where $0 \leq x \leq y \leq z \leq t$ , has exactly $2$ solutions in $\mathbb Z$ .

Mihai Baluna

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.