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English is not my native tongue.
19h

comment 
Does the Gamma function preserve integers?
@VítTuček: Thank you, that makes sense. 
Oct 18 
revised 
Fermat's little theorem with smaller powers
edited tags 
Oct 16 
comment 
Does the Gamma function preserve integers?
I think the same argument works with the simpler expression $\Gamma(z)\Gamma(1z)$. 
Oct 15 
revised 
Why do $12$ and $120$ occur very often in the denominators of $\zeta(n)$ for odd $n$?
added 1 character in body 
Oct 15 
revised 
Why do $12$ and $120$ occur very often in the denominators of $\zeta(n)$ for odd $n$?
edited tags 
Oct 15 
revised 
Why do $12$ and $120$ occur very often in the denominators of $\zeta(n)$ for odd $n$?
added 231 characters in body 
Oct 15 
answered  Why do $12$ and $120$ occur very often in the denominators of $\zeta(n)$ for odd $n$? 
Oct 9 
answered  Asking for an English version of a paper 
Sep 30 
awarded  Explainer 
Sep 25 
revised 
“Must read ”papers on analytic number theory
edited tags 
Sep 24 
awarded  Autobiographer 
Sep 23 
comment 
is $x_{n}\ll \overline{x}_{n}^{2}$?
@SylvainJULIEN: My example satisfies the stronger bound $x_n\leq n$ which clearly implies $\overline{x}_{n}<n/2$. 
Sep 23 
revised 
is $x_{n}\ll \overline{x}_{n}^{2}$?
added 25 characters in body 
Sep 23 
answered  is $x_{n}\ll \overline{x}_{n}^{2}$? 
Sep 22 
comment 
The angular distribution of the $(a,b)$ in $p = a^2+b^2$, and the distribution of the lattices corresponding to prime ideals
Sorry, I had a typo, I meant $L(1,\chi)\neq 0$. And yes, I meant equidistribution with respect to the uniform measure. 
Sep 22 
awarded  Nice Answer 
Sep 22 
comment 
The angular distribution of the $(a,b)$ in $p = a^2+b^2$, and the distribution of the lattices corresponding to prime ideals
I have to run now, but $L(1,\chi)\neq 1$ for unramified Hecke characters $\chi$ of $\mathbb{Q}(i)$ implies that $(a,b)$ is equidistributed in angle (in the sense that if you take a large disc etc.) 
Sep 21 
comment 
Solution or Reference Request for a Closed Form of the Sum
Do not expect any simple expression for the Legendre function. It is a complicated function in the sense that we cannot answer (even approximately) simple questions like: for a given $q$, how small is the smallest $a\geq 1$ with $\left(\frac{a}{q}\right)=1$ (cf. en.wikipedia.org/wiki/…). We like quadratic reciprocity (among other things) because it allows us to calculate the Legendre symbol in polynomial time. 
Sep 21 
comment 
Solution or Reference Request for a Closed Form of the Sum
@user170039: See my comment to your original post. 
Sep 20 
answered  Solution or Reference Request for a Closed Form of the Sum 