HMMT 2006 S14

Find the prime factorization of

$2006^{2} \cdot 2262-669^{2} \cdot 3599+1593^{2} \cdot 1337$

(No proof is necessary.)

Dataset text NuminaMath olympiads. 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.