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Hi guys need your help.

Sorry but I don't understand how to use latex. So really sorry for the writing. The question is if p is prime what values of $ a\leq p^{n}$ have $\text{gcd}(a, p^{n}) >1$?

Is it correct for me to assume that a could be multiple of p from $p^0$ to $p^{n-1}$, since all of them share common factor of at least $p$. But in this case we won't include $p^0$ since the question said so.

Is it correct? If it is, how do I properly make a point about my statement?

Dr C
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Stupid
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  • It is correct if you include $p^n.$ Moreover, you don't have to "assume" you have to "show". But you have done it partially. You can exclude the numbers that are not multiple of $p$ by the same reasons you have given. – mfl Nov 15 '14 at 21:09
  • They are all $kp$ where $k\le p^{n-1}$. If we are only interested in positives (which wasn't specified), we should further say $k\ge 1$. – André Nicolas Nov 15 '14 at 21:09
  • Ohhh thanks a lot! I finally understand it! – Stupid Nov 15 '14 at 21:15

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