Two questions here. I know the definitions, but cannot formulate a through proof.(adsbygoogle = window.adsbygoogle || []).push({});

1.a and b are positive integers. If a^3 | (is divisible by) b^2, then a | (is divisible by) b.

Now, by definition, I know that a^3*k=b^2, for some k. Also, I know that a * j = b for some j. But where do I go from here?

2.If p^a || (exactly divides) m, then p^ka || (exactly divides) m^k.

Again, by definition, p^a | (is divisible by) m and p^a+1 is not divisible by m. Also, p^ka | (is divisible by) m^k and p^ka+1 is not divisible by m^k+1.

This is all I can get. I just do not know where to go from here. Does anyone have any suggestions?? Thank you all, and you are all very smart on this website, if I have never mentioned that before!

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# Homework Help: Divisibility Questions

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