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 Oct 20 awarded Great Question Sep 9 answered Fields, closed under two operations Aug 5 comment Expected length of a sequence that contains all words of a given length. @ByronSchmuland I think that's the same ref leonbloy cited at the end of his answer below. Aug 5 revised Determine whether the argument is valid or invalid typesetting cleanup Aug 5 answered Determine whether the argument is valid or invalid Aug 4 comment N white and black balls and N boxes Probability Given $N$ new users posting $N$ new questions which are worded as demands rather than questions, what is the probability they are all homework problems? Jul 17 awarded Popular Question Jun 29 comment Fibonacci sequence - how to prove $a_n=\frac{1}{\sqrt{5}} ((\frac{1+\sqrt{5}}{2})^n-(\frac{1-\sqrt{5}}{2})^n)$ without induction This is given as a warmup in the free text by Wilf called generatingfunctionology. Jun 28 comment How to find generator in a finite group?what is generator? When I said, "suppose you can factor" the "you" is the OP who is (presumably) a human trying to solve a problem. I did not (and would not) say "suppose a factorization exists for $(p-1)$". Jun 28 answered How to find generator in a finite group?what is generator? Jun 25 awarded Informed Jun 24 comment practical arithmetic in prime factorizations Ross, I don't get your answer. You seem to be reiterating his idea rather than answering his question regarding the use of this technique in actual software. Jun 24 revised practical arithmetic in prime factorizations added 91 characters in body Jun 24 answered practical arithmetic in prime factorizations Jun 16 revised How many expected people needed until 3 share a birthday? added 208 characters in body Jun 15 revised Probability (usage of recursion) added 325 characters in body Jun 15 revised Probability (usage of recursion) added 325 characters in body Jun 15 answered Probability (usage of recursion) Jun 15 comment How to show that $\sum\limits_{k=1}^{n-1}\frac{k!k^{n-k}}{n!}$ is asymptotically $\sqrt{\frac{\pi n}{2}}$? @PeterR: Often mathematicians will use "elementary" to mean "does not use complex analysis". As you can see, "elementary" does not mean "easy." Jun 15 comment The sum $\sum\limits_{n \ge 0} \binom{m-1}{n} \frac{n!}{m^n} + \binom{n+1}{2}\binom{m-1}{n-1}\frac{(n-1)!}{m^n}$ is asymptotic to $\sqrt{9πm/8}$ Interesting. This immediately gives that three collisions occur in less than an expected $2 \sqrt{\pi m/2} = \sqrt{2\pi m}$. (In fact, I will guess that it's $15/8 \sqrt{\pi m/2}$.) Since $\sqrt{2\pi m}$ is the square root of the circumference of a circle of radius $m$, there is clearly a geometric proof we're missing. :)