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Aug
19
comment Bingo probability of a tie with 20 players
It seems very unlikely to get an answer by explicitly counting, but straightforward programming to get an answer by simulation.
Jul
29
comment Prime Numbers and a Two-Player Game
$L$ is given by oeis.org/A025043 .
Jul
22
comment asymptotics of Involutions recurrence relation
Looks like you read that section of Knuth more carefully than me. I stand corrected.
Jul
22
comment asymptotics of Involutions recurrence relation
The coefficient 7/24 is given in the reference of Knuth cited by Wimp and Zeilberger (section 5.1.4 in volume 3), but the computations are quite involved.
Jul
13
comment “Binomiable” numbers
A list of these numbers is at oeis.org/A006987 - there doesn't seem to be much there. In particular, if there were a nice criterion I'd expect it to be listed there. But it's a fun problem - keep playing around with it!
Jul
6
comment Is there something special about 2015?
I would vote this up but it currently has 77 upvotes.
Jul
6
comment Find the parameter $m$ such that the number always be perfect square.
This solution implicitly uses the fact that $x^2 + a$ is square for all integers $x$ and only if $a = 0$. This needs a proof, although it's easy: $a^2 + a$ is not square because it's between the consecutive squares $a^2$ and $(a+1)^2$. (Note this holds even if $a$ is negative.)
Jun
22
comment Generating function solution to previous question $a_{n}=a_{\lfloor n/2\rfloor}+a_{\lfloor n/3 \rfloor}+a_{\lfloor n/6\rfloor}$
OEIS reference: oeis.org/A007731
Jun
5
comment Is there a closed form for $\sum_{n=0}^{+\infty} \frac{1}{\sqrt {n!}}$?
It seems quite unlikely. See mathforum.org/kb/message.jspa?messageID=5628902 or wilmott.com/messageview.cfm?catid=34&threadid=44616 (which can be found by computing the sum numerically and googling the resulting value).
May
14
comment Prove that using generating function:For any $n ,k\in N$, the number of partitions of $n$ into parts
If you're being asked this, I suspect you've seen the generating-function proof for the case $k = 1$ - that is, that the number of partitions into parts which appear at most 1 time ("partitions into distinct parts") is the same as the number of partitions into parts not divisible by 2 ("partitions into odd parts"). Can you generalize this proof?
May
11
comment Find a linear reccurrence relation where a(n) is the number of subsets of {1,2,3,…,n} not containing three consecutive numbers.
This is a duplicate of math.stackexchange.com/questions/86249/… , although that question wasn't answered so I recommend leaving this one open.
Apr
29
comment If $n$ is composite, then $((n-1)!)^2 \equiv 0 \pmod n$
4 is the only counterexample: see e. g. Benoit Cloitre's comment at oeis.org/A046022
Apr
28
comment Find the probability of the following event
This, with slightly different numbers, is Kahneman and Tversky's taxicab problem: en.wikipedia.org/wiki/…
Apr
10
comment Compute $\sqrt[7]{0.999}$ to three decimal places.(From Gelfand's Algebra text.)
I don't agree with your assumption; my assumption is that Gelfand was looking for a smarter answer like mine, given that the numbers involved are so close to 1. (If he'd asked, say, to compute the cube root of 3.257, then I'd expect that he was looking for the long-multiplication answer.) But I can't prove this.
Feb
24
comment Is $\int_0^\infty x^{a-1} (1-x)^{b-1} e^{t-cx} dx$ integrable?
Thanks! I hadn't realized that your context was a beta distribution, and this was the first thing that came to mind.
Jan
30
comment Explain why catastrophic cancellation happens
I'm seeing the same thing in R. This supports the idea that this is an issue with floating-point numbers.
Jan
29
comment Why is Multiplicative Notation Used for Groups (Instead of Additive)?
I'm not sure I'd call this "multiplicative" notation - we don't explicitly write out the multiplication sign. I think that this is a case of juxtaposition having two meanings, multiplication (when used for numeric variables) and an arbitrary group operation.
Jan
20
comment Mathmatical notation for a term of a polynomial
I think that's the closest there is to a standard notation. (But I honestly wouldn't use it without definition unless speaking to an audience of people who deal with generating functions all the time.)
Jan
15
comment Find a quartic (degree 4) polynomial with integer coefficients whose roots are the primitive 12th roots of unity
The polynomial $(z-\alpha_1) (z-\alpha_2) \cdots (z-\alpha_n)$ has roots $\alpha_1, \alpha_2, \cdots, \alpha_n$.
Jan
14
comment Expectation of maximum of Binomial RVs
possible duplicate of Bounds for the maximum of binomial random variables