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10h
revised Arithmetic functions of particular type
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10h
comment Arithmetic functions of particular type
This is really von Mangoldt's formula. $\psi_0(x)$ and $\psi(x)$ are not the same.
10h
comment Arithmetic functions of particular type
The error in counting primes is due to their irregularity. $\psi(x)\sim \theta(x)$ even though one counts prime powersand the other does not.
10h
revised Arithmetic functions of particular type
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11h
answered Arithmetic functions of particular type
19h
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.
20h
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.
20h
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--
20h
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.
23h
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.
23h
revised Finite coloring of an interval
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1d
comment Finite coloring of an interval
I have assumed "the number of intervals of different colors" counts red/blue/green/red as 4 intervals.
1d
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
answered Finite coloring of an interval
2d
accepted Showing $\gamma < \sqrt{1/3}$ without a computer
2d
comment About primitive roots and primes.
@RobertSoupe: André Nicolas' comment suggests that OP will still be unsure.
2d
revised Source of Hardy-Littlewood's 2nd Conjecture
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2d
awarded  Constituent
2d
revised Source of Hardy-Littlewood's 2nd Conjecture
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Dec
19
revised Source of Hardy-Littlewood's 2nd Conjecture
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