KöMaL 2023 B5304

$a)$ Are there positive integers $a$ and $b$ such that $a+b \mid a^2+b^2, \text{but} a+b \nmid a^4 + b^4?$ $b)$ Are there positive integers $a$ and $b$ such that $a+b \mid a^4+b^4, \text{but} a+b \nmid a^2+b^2?$