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Jul
10
awarded  Enlightened
Jul
10
awarded  Nice Answer
Jul
2
awarded  Curious
Jul
2
comment What five odd integers have a sum of $30$?
That is neither 5 numbers nor "summed together".
Jun
27
comment How to tell if a Fibonacci number has an even or odd index
Yes, as I see it, the question is how efficient doing that is, and whether that's the most efficient method possible. See MJD's answer (which IMO is not complete yet). (BTW, the OP does mention the $F_1 = F_2$ exception, and is presumably fine with a rule that applies only for $n > 2$.)
Jun
27
comment How to tell if a Fibonacci number has an even or odd index
I think the part "compute the index of the Fibonacci number" is what the question is about.
Jun
19
comment Intuitively, what separates Mersenne primes from Fermat primes?
@pew: The "random" heuristic is a very powerful one, coming from the deep and profound prime number theorem. With appropriate modifications, it is consistent with all results proved so far about prime numbers. See for instance here, here, here...
Jun
18
comment Intuitively, what separates Mersenne primes from Fermat primes?
@PedroTamaroff: $2^n + 1$ is prime only when $n$ is a power of $2$. And $2^n - 1$ is prime only when $n$ is a prime numer. So the Mersenne primes are precisely those primes of the form $2^n - 1$, and the Fermat primes precisely those of the form $2^n + 1$. (This is differnet from a hypothetical like "primes of the form $n$", as that would include more primes.)
Jun
18
comment Finding Probability of a falling fan
Very closely related to this question: Why is not the answer to all probability questions 1/2.
Jun
17
comment Blood relation - How A is related to B
Actually, because B's mother is D, it means that A's mother is also D. Definitely something wrong with the problem statement, hopefully!
Jun
17
comment Blood relation - How A is related to B
@Fabien: Why can't A be male (and so A = B)? And how does that fit with the first statement?
Jun
13
comment Find a generating function for $\sum_{k=0}^{n} k^2$
The sum diverges; also it's a single expression and not a sequence. Perhaps you mean "find a generating function for $\sum_{k=0}^{n} k^2$".
Jun
10
comment Ramanujan's personification of small positive integers
en.wikipedia.org/w/… — using things there are $n$ of, to denote the number $n$, was a standard practice in classical Indian mathematics. I'm not sure whether Ramanujan had encountered any classical Indian mathematics though, so I have a tiny suspicion that the author of The Man Who Knew Infinity just got things a bit mixed up. (Or maybe Ramanujan did arrive at the same convention by himself; we know he did that with a lot of mathematics!)
Jun
8
comment How does a row of zeros make a free variable in linear systems of equations?
A row of zeroes (or, in general, the matrix's row rank being less than the number of columns) means that there are not enough equations to completely determine all the variables. In this case, you can pick any of the three variables as a free variable, and determine the other two in terms of it. Sorry if this isn't clear; maybe someone will post a more clear answer.
Jun
5
comment Is it true that $\binom{n}{m} \binom{k}{\ell} \le \binom{n+k}{m+\ell}$?
Thanks, I get it now. In full detail (in addition to your explanation): $$\sum_{k\ge 0}\sum_{\ell=0}^k \frac{\binom{n}{m} \binom{k}{\ell}}{\binom{n+k}{m+\ell}}\frac{a^k s^k}{k!} = \sum_{k\ge 0}\frac{a^k s^k}{k!}\sum_{\ell=0}^k \frac{\binom{n}{m} \binom{k}{\ell}}{\binom{n+k}{m+\ell}} = \sum_{k\ge 0}\frac{a^k s^k}{k!} {n+1+k\over n+1}$$ $$= \sum_{k\ge 0}\frac{a^k s^k}{k!} + \frac1{n+1}\sum_{k\ge 0}k\frac{a^k s^k}{k!} = \exp(as)+\frac{as \exp(as)}{n+1}$$
Jun
5
comment Is it true that $\binom{n}{m} \binom{k}{\ell} \le \binom{n+k}{m+\ell}$?
How do you get the second equation from the first?
Jun
4
comment How do you evaluate $a^b$ where b is irrational using only basic operators.
Pick a rational approximation $r$ to $b$, and evaluate $a^r$. For better results, start with better rational approximations.
May
29
comment The Probability of Catching Criminals
@Anonymous: I'm not sure I understand the question. Could you clarify? (You could post it as a new question, too.)
May
29
comment The Probability of Catching Criminals
@Anonymous: What is the difference you're thinking of between "number of pairs" and "possible number of pairs"? And yes, with $N$ people there are $\binom{N}{2}$ pairs, but over $T$ time units of buying, there are $T\binom{N}{2}$ opportunities for a pair of people to buy the same set of items at the same time. (For each pair of people, there are $T$ times when they could buy the same thing.)
May
27
comment Does anyone know why this inclusion exclusion calculation isn't working?
@askyle: Sure, feel free.