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Mar
19
comment Solution to a linear system
I would advise you to see your teacher and ask whether a working knowledge of linear algebra is a prerequisite for the course and, if it is, drop the course and take linear algebra first.
Mar
19
comment Properties of Entire Functions
No source, no sign of effort by OP, no indication of what OP knows, where OP gets stuck ... voting to close.
Mar
18
comment Binomial formula for $(x+1)^{1/3}$ (related to Newton's binomial theorem)
If there isn't a solution, there isn't a problem. Not every complex mathematical expression has a simpler form. I think you have to live with what you have.
Mar
18
comment evaluate $\phi(50!)$
No one knows a better way to get $\phi$ than by factorization. Indeed, in many contexts the two problems are equivalent, in that if you can do either one then you can do the other just as fast.
Mar
18
comment Binomial formula for $(x+1)^{1/3}$ (related to Newton's binomial theorem)
I don't think you can write anything for $(2)(5)\cdots(3j-4)$. Why do you feel you need to?
Mar
18
comment Statements true for all n Vs. statements true as n->infty
The definition of the notation $\cap^{\infty}A_i$ is the things that are in $\cap^nA_i$ for all $n$.
Mar
18
answered Can a sequence of finite subsets of $\mathbb R$ converge to $\mathbb R$?
Mar
18
comment Is there a list of all known Sophie Germain prime numbers?
$512$ bytes is, what, about $1200$ digits? If you have the right software and hardware, I don't think it's hard to generate primes of that size. On a mobile phone, I'm not so sure. I see you have found primes.utm.edu --- there are links there to computational questions.
Mar
18
comment Markov chain property
@Djaian, I missed that, but I think the gap is easily filled. If there a path from $i$ to $j$ in $m$ steps, with $m\gt N$, then some state $k$ shows up twice in that path, so you could shorten the path by leaving out all the states between the two appearances of $k$. So, the shortest path can't visit any state twice, so it has length at most $N$.
Mar
18
answered What is a relationship between sets and Trinomial Coefficient?
Mar
18
comment Population Transition Matrix
(c) asked for the eigenvalues and the eigenvectors; you found the former, but not the latter. You need an eigenvector for the eigenvalue $1$, with components adding to $10,000$.
Mar
18
comment Analogy for Cosets, Ideals, and Quotient Rings
You're asking us to write a book. This site works better with one question per question, with a specific answer expected.
Mar
18
comment Article about primes.(Revised)
My algorithm is to look it up on the internet.
Mar
18
answered Markov chain property
Mar
18
comment Find $C$ if $B(B-C)=23$. $B$ and $C$ are positive integers.
I would say $1$ into $23$ is $23$, but apparently customs differ. Anyway, that tells you $1\times23=23$. Are there any other possibilities? Once you have all the possibilities, you have all the possible values of $B$, right?
Mar
18
comment Showing that a certain inequality holds for all $ x \in \mathbb{R} $ and $ n \in \mathbb{N} $.
"high school math problem" What does that mean? Homework problem from a high school math class? Competition problem to get into a high school math program?
Mar
18
answered Article about primes.(Revised)
Mar
18
comment Article about primes.(Revised)
"A detailed canonical answer is required"? "I expect suggestions which are not from previous research"??? You expect people to invent, on the spot, brand new relations between primes and other topics, so you can write an article about primes? Hoo, boy!
Mar
18
answered Solving a non-linear equation of 3 unknowns
Mar
18
comment Asymptotic Growth of Unitary Totient
And I would prefer to have a pony. But maybe you can read through what Will has done, and come up with your own clear and unified treatment, which you can then post here as a new answer.