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Math Help - Number Theory

  1. #1
    Junior Member
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    Question Number Theory

    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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  2. #2
    Super Member PaulRS's Avatar
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    1. If b=n^{2} and a=n^3 for any integer n\neq{0} and n\neq{\pm{1}}then a^2=b^3 so a^2|b^3 but obviously a|b doesn't hold

    2. This is true.By Euclid's Lemma p|a. Suppose <br />
p^s<br />
is the max. power of p dividing a, since p^4|a^2 it follows that 2s\geq{4} so s\geq{2}, therfore p^2 divides a(since s is greater or equal than 2)
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  3. #3
    Newbie Catherine Morland's Avatar
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    Counterexample for first problem: a = 8, b = 4.
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