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 Jun 9 revised Can a group of order $55$ have exactly $20$ elements of order $11$? (Clarification) edited body Jun 9 asked Can a group of order $55$ have exactly $20$ elements of order $11$? (Clarification) Jun 9 comment Can a group of order $55$ have exactly $20$ elements of order $11$? How do you get that there would be 34 elements remaining with order 5? Jun 9 comment Showing a compact metric space has a countable dense subset I'm struggling with why $d(x,y)$ has to be less than $1/n$. If the definition of a dense set just requires that another point of $D$ lie in some open neighbourhood of $x \in X$, couldn't it be possible that $y$ is still in $B(x,\epsilon)$ but that the distance between the two points is not less than $1/n$? Jun 8 accepted Determining whether or not a group has an element of a specific order Jun 8 accepted What can we say about the order of a group given the order of two elements? Jun 8 asked Determining whether or not a group has an element of a specific order Jun 8 comment What can we say about the order of a group given the order of two elements? To generalize, do I just take all divisors of $n$? If every nontrivial element has the same order, then it must be a $p$-group because the only divisors of $p$ are $1$ and $p$ itself (this means the group $G$ in my problem is certainly not a $p$-group). Is this correct? Jun 8 asked Showing a compact metric space has a countable dense subset Jun 7 comment What can we say about the order of a group given the order of two elements? could we say it has an element of order 2, 3, and 5? $x^6 = (x^2)^3 = (x^3)^2$, and similarly for $x^{10}$. I know that doesn't say much about $G$, but I'm just trying to figure out what more can be said. Jun 7 comment What can we say about the order of a group given the order of two elements? @MartinArgerami Aren't they saying the same thing? Sorry, I was trying to be more formal about it. Thanks for pointing it out Jun 7 revised What can we say about the order of a group given the order of two elements? added 26 characters in body Jun 7 asked What can we say about the order of a group given the order of two elements? Jun 5 revised Central Limit Theorem Problem changing title, adding tag Jun 5 suggested approved edit on Central Limit Theorem Problem Jun 3 comment $f(x) = \frac {e^{2x-1}} {(1+e^{2x-1})}.$ What is the value of $f(1/2009) + f(2/2009) + … + f(2008/2009)$? @CalvinLin If you don't mind me asking, what is the difference between brilliant.org and sites such as art of problem solving? Jun 3 comment solve system of linear congruences mod 13 Ah, okay. Thanks. Btw, when you multiply $-5$ to equation $I$, did you mean to write $-5$ on the RHS? Jun 3 comment solve system of linear congruences mod 13 In my textbook, multiplication by a scalar m on $a \equiv b \pmod{c}$ gives $am \equiv bm \pmod{mc}$. Why is it that you don't multiply the modulus number $13$in the beginning of your solution? Jun 2 comment Showing existence of an element with order $p$ It's because the order of an element of a group has to divide the order of the group. The only possible divisors of $p^n$ are $1,p^2,\cdots, p^n$. The only element that has order 1 is the identity $e$. So we just pick an element not equal to $e$. Is this correct? Jun 2 comment Has anyone studied this operator? @KeyIdeas I had read one of your posts about Gauss's Algorithms I was wondering if it was called something else officially. I'd simply like to read up on it, but I can't find its wikipedia page.