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.
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1. If and for any integer and then so but obviously doesn't hold 2. This is true.By Euclid's Lemma p|a. Suppose is the max. power of p dividing , since it follows that so , therfore divides (since s is greater or equal than 2)
Counterexample for first problem: a = 8, b = 4.
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