AlanH
Reputation
1,181
Top tag
Next privilege 2,000 Rep.
 Jun7 revised What can we say about the order of a group given the order of two elements? added 26 characters in body Jun7 asked What can we say about the order of a group given the order of two elements? Jun5 revised Central Limit Theorem Problem changing title, adding tag Jun5 suggested approved edit on Central Limit Theorem Problem Jun3 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? Jun3 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? Jun3 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? Jun2 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? Jun2 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. Jun2 comment Showing existence of an element with order $p$ Sorry, I was referring to how I need to pick that $a$ such that the order is one of $p^1, \dots, p^n$. Jun2 comment Find all positive integers $x$ such that $13 \mid (x^2 + 1)$ Is there a general form of the first sentence you stated? Jun2 accepted Find all positive integers $x$ such that $13 \mid (x^2 + 1)$ Jun2 revised Find all positive integers $x$ such that $13 \mid (x^2 + 1)$ added 39 characters in body Jun2 asked Find all positive integers $x$ such that $13 \mid (x^2 + 1)$ Jun2 comment Showing existence of an element with order $p$ Do you mind explaining further? I'm still not sure what to do. Jun2 accepted Showing existence of an element with order $p$ May29 asked Showing existence of an element with order $p$ May27 accepted Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$ May27 comment Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$ but $r$ is indexed May27 comment Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$ In my text, I have an identity $\sum_{r\geq 0} \binom{r + n}{r} x^r = 1/(1-x)^{n+1}$ This may be the cause of my confusion, but is this identity correct and is it equivalent to the one you used?