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Jul
21
revised Continuous and bounded imply uniform continuity?
deleted 1 character in body
Jul
21
revised Given that $p$ is an odd prime, is the GCD of any two numbers of the form $2^p + 1$ always equal to $3$?
edited title
Jul
21
revised Continuous and bounded imply uniform continuity?
added 2 characters in body
Jul
21
comment Proof of Wilson's Theorem using concept of group.
I deleted the comment @joriki was mentioning. It said $2(p-2)$ is congruent to $-4\bmod p$ which is not always $-1\bmod p$.
Jul
21
answered Proof of Wilson's Theorem using concept of group.
Jul
21
comment Limit of $f$ at $(0,0)$ vs limits of $f(x,kx)$ when $x\to0$
because each straight line is independent from the rest?
Jul
21
revised Continuous and bounded imply uniform continuity?
added 283 characters in body
Jul
21
answered Continuous and bounded imply uniform continuity?
Jul
20
comment How many ways are there to shake hands?
Oh, I'm sorry about that. For some reason my brain didn't parse that part of the question, I just realized it now, it must be the heat.
Jul
20
comment How many ways are there to shake hands?
For example notice $1,2,3\dots k$ and $1,k,k-1,k-2\dots 3,2$ give us the same cycle. Since there are $(k-1)!$ permutations of the elements $2,3,4,5\dots k$ and to every two of these permutations there corresponds a cycle, we deduce there are $\frac{(k-1)!}{2}$ cycles on the elements $(1,2,3,4,\dots k)$
Jul
20
comment How many ways are there to shake hands?
well, if you have $k$ vetices $1,2,3\dots k$ how many ways can we add edges so that they form a cycle? The most usual cycle would be to connect $1$ with $2$ and $k$ and to connect $k$ with $k-1$ and $1$. And connect every other number $j$ with $j-1$ and $j+1$. This is one of the possible cycles. But there are many other cycles. You can describe a cycle by giving a list that starts in $1$ and includes each vertex $1$. For example: $1,2,3,4\dots k$ describes the cycle I mentioned at the beginning. Every cycle can be characterized with a list like that. However each cycle has two lists.
Jul
20
revised How many ways are there to shake hands?
added 91 characters in body
Jul
20
revised How many ways are there to shake hands?
added 91 characters in body
Jul
20
revised How many ways are there to shake hands?
added 91 characters in body
Jul
20
comment How many ways are there to shake hands?
No, it isn't a duplicate.
Jul
20
answered How many ways are there to shake hands?
Jul
20
awarded  Necromancer
Jul
20
awarded  Nice Question
Jul
20
revised Subgroups of $S_n$ with exactly one fixed point for each element all have the same fixed point.
edited title
Jul
19
revised How to replace addition with multiplication to find the next integer value?
added 6 characters in body; edited tags