I have an exercise that I don't know how to solve. I tried to solve it in many ways, but I didn't get any progress in proving or disproving this... The exercise is:
Prove or disprove: if $p$ is a prime number, if $a$ and $b$ are native numbers and $$ a^2 = b^3 $$ and if $p \mid b$, then $$ p^3 \mid a .$$
If someone has a proof to this exercise I would really appreciate it.