We say an integer $a$ divides $b$ if $\frac{b}{a}$ is an integer. (Another way to think about this is there is no remainder when $b$ is divided by $a$.)
Part 1: Are there positive integers $a$ and $b$ such that $a+b$ divides $a^2+b^2$ but $a+b$ does not divide $a^4+b^4$
Part 2: Are there positive integers $a$ and $b$ such that $a+b$ divides $a^4+b^4$ but $a+b$ does not divide $a^2+b^2$