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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.
Jun
2
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 $p^1, \dots, p^n$.
Jun
2
comment Find all positive integers $x$ such that $13 \mid (x^2 + 1)$
Is there a general form of the first sentence you stated?
Jun
2
accepted Find all positive integers $x$ such that $13 \mid (x^2 + 1)$
Jun
2
revised Find all positive integers $x$ such that $13 \mid (x^2 + 1)$
added 39 characters in body
Jun
2
asked Find all positive integers $x$ such that $13 \mid (x^2 + 1)$
Jun
2
comment Showing existence of an element with order $p$
Do you mind explaining further? I'm still not sure what to do.
Jun
2
accepted Showing existence of an element with order $p$
May
29
asked Showing existence of an element with order $p$
May
27
accepted Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$
May
27
comment Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$
but $r$ is indexed
May
27
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?