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2h
comment primes of the form $4k+3$ and sums of squares
A good account of this topic is in H. Edwards 'Fermat's Last Theorem', which includes a proof of this and similar results.
2h
comment Find the values of the positive integers $n$ such that: $\frac{(-\sqrt{3}+2)^{n+1}+(\sqrt{3}+2)^{n+1}}{4n+3}$ is positive integer
@JackD'Aurizio: Does the currently accepted answer seem like a correct answer to you? The problem is interesting and difficult and you made what seemed reasonable observations. I am confused by the status...
2h
comment Find the values of the positive integers $n$ such that: $\frac{(-\sqrt{3}+2)^{n+1}+(\sqrt{3}+2)^{n+1}}{4n+3}$ is positive integer
For the first ten terms of the numerator I get $14, 52, 194, 724, 2702, 10084, 37634, 140452, 524174, 1956244.$ For $2^{n+2}Re(1+i\sqrt{n})^{n+1}$ I get for n =1 to 10: 0, -80, -256, 2624, 22528, -96512, -2031616, 1672192, 204210176, 493367296. These don't correspond to the numerator or to the numbers I get when I compute the full expression--the integers being 2,1214,...etc. Brief hint or guidance appreciated.
2h
comment Find the values of the positive integers $n$ such that: $\frac{(-\sqrt{3}+2)^{n+1}+(\sqrt{3}+2)^{n+1}}{4n+3}$ is positive integer
You changed the form of the numerator, right? I haven't looked at this carefully yet. Are you saying this is the answer to the problem? I was surprised to see it accepted but will add my upvote if it's right. Thanks--
2h
comment Find the values of the positive integers $n$ such that: $\frac{(-\sqrt{3}+2)^{n+1}+(\sqrt{3}+2)^{n+1}}{4n+3}$ is positive integer
The user who posted the answer you accepted didn't seem to regard it as a complete response to the question--just a comment that was too big for comment space. Did you accept it because you think it's correct? I haven't looked at it carefully.
5h
comment Finite coloring of an interval
@ErelSegalHalevi: The restriction of the second paragraph we might as well call the "avoid having infinite intervals" property. Maybe something like continuity plus (?) in the third paragraph could work although monotonicity seems excessive. This is a nice question and I hope you get other responses. The problem with basic answers is that there are a collection of pathological functions that can defeat desired properties in surprising ways. The challenge is to find something both suff. and necc.
6h
comment Finite coloring of an interval
I have assumed "the number of intervals of different colors" counts red/blue/green/red as 4 intervals.
7h
comment On riemann zeta function
"What is the importance of..." is very broad and vague. I haven't voted to close but it's really too vague.
1d
comment About primitive roots and primes.
@RobertSoupe: André Nicolas' comment suggests that OP will still be unsure.
Dec
16
comment Extending the zeta function to semiprimes, etc.
As always, the opinion of someone working in this area is the gold-standard and you could cross-post at MO. There is no linear trail from Landau to current research and there are probably hundreds of papers in this area so it's a long process to search for them.
Dec
16
comment Extending the zeta function to semiprimes, etc.
The topic mostly I think falls under the rubric of Dirichlet series but you would have to sift out the material dealing with arithmetic sequences which is a different topic.
Dec
16
comment Extending the zeta function to semiprimes, etc.
This is possibly on point. On the Residue Class Distribution of the Number of Prime Divisors of an Integer. Coons and Dahmen, Nagoya Math j. 202, 2011, 15-22.
Dec
16
comment Prove that $\frac{(p^{n}-1)(p^{n}-p)…(p^{n}-p^{n-1})}{n!} \in \mathbb{N}$ with $p$ a prime number and $n \in \mathbb{N}$
I think it's good to have this here even if it's the un-asked for version. +1.
Dec
15
comment A deep understanding of the Fourier transform
The uncertainty Principle: A Mathematical Survey by Folland and Sitaram, J. of Fourier Analysis 1997. I found this helpful. There is also a very accessible section in a book with the misleading title, "Wavelets Made Easy."
Dec
15
comment Unusual pattern in the distribution of odd primes
May 12 of this year (my eyes aren't so good). My only concern is that work is being repeated. It's a very good paper and worth reading. And there is similar material relating to semi-primes and polynomials.
Dec
14
comment Unusual pattern in the distribution of odd primes
I don't get it. At MO you say in a comment under a nearly identical question from May 2012 that you had read 'Prime Number Races.' But this question is precisely on that paper's topic--as though you had never encountered this before, much less read the paper. @GerryMyerson noted that you had already asked the question on MSE, and he had recommended 'Prime Number Races.' I went back and looked for related questions on GRH-AP and semi-primes but I think you have seen this all before...?
Dec
14
comment Unusual pattern in the distribution of odd primes
mathoverflow.net/questions/165887/….
Dec
11
comment Numbers with special factorisation
But I don't know what you mean when you say you are looking for solutions.
Dec
11
comment Numbers with special factorisation
This is usually referred to as $p_n$-primorial. It is written $p_n!!$ or $p_n\#.$ The numbers of this type are 2,6,30,210,... etc.
Dec
11
comment Reference for Analytic Number Theory
You might consider getting a copy of Jameson's 'The Prime Number Theorem' and reading it. I haven seen anything along the lines of your request but it may exist.