2024 IMO Shortlist N4

Determine all positive integers $a$ and $b$ such that there exists a positive integer $g$ such that $\gcd(a^n+b,b^n+a)=g$ for all sufficiently large $n$.

确定所有正整数 $a,b$，使得存在正整数 $g$，对所有充分大的 $n$ 都有 $\gcd(a^n+b,b^n+a)=g$。