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English is not my native tongue. German is not my native tongue. French is not my native tongue.
19h

comment 
Counting number of points in a lattice with bounded sup norm
@SJY: I am glad I could help. If you find any of my posts useful, please drop me a point for it. Thanks! 
1d

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Counting number of points in a lattice with bounded sup norm
@SJY: The volume of $B$ is $\prod_{l=1}^j(t_lr_l)$ times $Vol_j(B')$, where $B'=[0,1]v_1+\dots+[0,1]v_j$ is the parallelepiped spanned by the vectors $v_1,\dots,v_j$. In order to find $Vol_j(B')$, follow my comment of Apr 5 at 3:42. At any rate, you can read about the Lebesgue measure in many textbooks, e.g. in Rudin: Real and complex analysis. 
1d

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Counting number of points in a lattice with bounded sup norm
@SJY: The $j$volume is the Lebesgue measure on the underlying $j$dimensional subspace. I called it $j$volume to distinguish it from the Lebesgue measure on the full space. 
1d

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Integer solution to the equation
I answered the problem in the negative. See below. 
2d

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Primes as uncorrelated random variables
The Wikipedia article does not use the word "proof" in that context. So the quotation mark is misleading here. Without the quotation mark, it would be equally misleading, so I suggest you change the first sentence. A more serious problem with your post is that it does not contain a wellformulated mathematical question. To clarify: no proof of Goldbach's conjecture would consider the primes random variables, because they are not random variables. 
2d

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An upper bound for the length of the continued fraction expansion of $\sqrt d$
@GeraldEdgar: In analytic number theory, $f(x)=\Omega(g(x))$ means that $f(x)=o(g(x))$ is false, and I followed that convention. See en.wikipedia.org/wiki/… 
2d

revised 
An upper bound for the length of the continued fraction expansion of $\sqrt d$
added 134 characters in body 
2d

answered  An upper bound for the length of the continued fraction expansion of $\sqrt d$ 
Apr 16 
awarded  Nice Answer 
Apr 15 
answered  A variant of Goldbach Conjecture 
Apr 15 
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What math do I need to know in order to understand basic trigonometry?
This site is for research level questions. For general questions in mathematics see math.stackexchange.com 
Apr 14 
revised 
Is every positive integer a sum of at most 4 distinct quartersquares?
deleted 5 characters in body 
Apr 14 
revised 
Is every positive integer a sum of at most 4 distinct quartersquares?
improved the presentation 
Apr 13 
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Equivalence of Polignac to finite Goldbach?
@GerryMyerson: I think I got confused by history a bit. At any rate, Hardy and Littlewood did conjecture an asymptotic formula for Goldbach's conjecture, and they gave a heuristic for it in their paper "Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes". In the same paper, they also gave an asymptotic formula for Polignac's conjecture, with a similar heuristic and a similar shape. See Conjecture A (on page 32) and Conjecture B (on page 42) in the paper (available online as fuchsbraun.com/media/8cdd73c813c342f8ffff80d1fffffff0.pdf). 
Apr 12 
answered  Equivalence of Polignac to finite Goldbach? 
Apr 11 
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Has this strong number theoretic conjecture of Euler been proved, and where could I find such a proof?
Nice find indeed. A similar treatment can be found in euler.genepeer.com/eulerspentagonalnumbertheorem 
Apr 11 
revised 
Has this strong number theoretic conjecture of Euler been proved, and where could I find such a proof?
Fixed spelling. 
Apr 10 
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On successive minima and basis of a lattice
@SJY: I don't know such an example. 
Apr 9 
revised 
Is $1/\max(i,j)$ a bounded matrix on Hilbert spaces?
fixed spelling 
Apr 9 
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Is $1/\max(i,j)$ a bounded matrix on Hilbert spaces?
This is very nice! 