Prove or Disprove the following statements
If a,b in Z bot greater than 0, and a^2|b^3, than a|b
If a in Z, a>0, p is prime, and p^4|a^2, then p^2|a.
1. If $\displaystyle b=n^{2}$ and $\displaystyle a=n^3$ for any integer $\displaystyle n\neq{0}$ and $\displaystyle n\neq{\pm{1}}$then $\displaystyle a^2=b^3$ so $\displaystyle a^2|b^3$ but obviously $\displaystyle a|b$ doesn't hold
2. This is true.By Euclid's Lemma p|a. Suppose $\displaystyle
p^s
$ is the max. power of p dividing $\displaystyle a$, since $\displaystyle p^4|a^2$ it follows that $\displaystyle 2s\geq{4}$ so $\displaystyle s\geq{2}$, therfore$\displaystyle p^2$ divides $\displaystyle a$(since s is greater or equal than 2)