Esteban Crespi
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 Dec 1 comment Galois group and the Quaternion group I have corrected the right hand side of $(\theta^2-6-2\sqrt{3})^2$, sorry for that. I have also added some computations in the end to help you with the automorphisms. Dec 1 revised Galois group and the Quaternion group Added explanation Nov 30 answered Galois group and the Quaternion group Nov 10 comment Early history of lower bounds on the prime counting function I'm sorry I've made an incorrect statement, I could not edit it so I have removed it. Nov 8 awarded Yearling Nov 7 answered Cover a disk with thin rectangles Nov 6 comment What would be complexity of computing $3^{n^n}$? If you are computing $3^{n^n}$ modulo an integer $M$ and you know it's totient function $\varphi(M)$ then you can compute $n^n$ in $O(\log n)$ multiplications $\pmod{ \varphi(M)}$ and then rise $3$ to the result in $O(\log M)$ multiplications mod $M$ finding the result in polynomial time. The problem is to find $\varphi(M)$. Some times it can be done in polynomial time (for example if $M$ is prime then $\phi(M)=M-1$), but in general if $M$ is composite finding $\varphi(M)$ is equivalent to finding the factorization of $M$. Nov 3 revised Half the rationals? Added a generalization Nov 3 answered Half the rationals? Nov 1 comment Half the rationals? A good candidate for your set $X$ with a very simple description is the set of reduced fractions $a/b$ with $$a\cdot b \equiv 0 \pmod{3}$$ Nov 1 comment Half the rationals? I think there something missing in the right hand side of the inequality $\sum_{k=1}^{n-1} a_k\phi(k) < 1/2$, I suppose you mean $<\frac{1}{2}\sum_{k=1}^{n-1} \phi(k)$? On the other hand, even if it is probably true, I can't see how to prove that this construction works for all the intervals $Y$. Nov 1 comment Half the rationals? I think that the proportion of fractions with even numerator and denominator bounded by $N$ is aproximately one third, and the same for even denominator. Oct 15 revised Tiling a minimal perimeter region with $n$ unit squares Sketch of proof Oct 15 answered Tiling a minimal perimeter region with $n$ unit squares Jul 19 answered Solving a polynomial modulo an integer Jun 8 awarded Caucus Apr 19 revised Burgess on quadratic residues and non-residues edited body Apr 19 comment Burgess on quadratic residues and non-residues No that's an error I correct it Apr 19 comment Burgess on quadratic residues and non-residues I have edited the answer to make it more clear. I hope this helps. Apr 19 revised Burgess on quadratic residues and non-residues added 1406 characters in body