Esteban Crespi
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 Dec22 awarded Revival Dec22 answered Generalizing Ramanujan's proof of Bertrand's Postulate: Can Ramanujan's approach be used to show a prime between $4x$ and $5x$ for $x \ge 3$ Dec18 awarded Nice Question Nov8 awarded Yearling Jun21 revised How prove that:$\varphi(2)+\varphi(3)+\varphi(4)+\cdots+\varphi(n)\ge\frac{n(n-1)}{4}+1$ I have rewritten the proof as the original was very confusing and contained some incorrect statements. Jun21 revised How prove that:$\varphi(2)+\varphi(3)+\varphi(4)+\cdots+\varphi(n)\ge\frac{n(n-1)}{4}+1$ deleted 2 characters in body Jun21 answered How prove that:$\varphi(2)+\varphi(3)+\varphi(4)+\cdots+\varphi(n)\ge\frac{n(n-1)}{4}+1$ Jun4 comment Can this sum be simplified to closed form? I'm not sure how to prove it but it seems that the following might be true: set $S(L,b) = \sum_{a=0}^{L-1} \lfloor ab/L\rfloor^2$, and write $L = nb+t$ then $S(L,t) = n(n+1)(2n+1)/6 + S(t,b)$. May4 comment Do these inequalities regarding the gamma function and factorials work? Is $x$ an integer? if not what does it mean $n \vert (x+1)$? Apr2 comment Best Fake Proofs? (A M.SE April Fools Day collection) It seems that Euler himself was confused with this. See [here]( webspace.utexas.edu/aam829/1/m/Euler_files/EulerMonthly.pdf) Mar9 awarded Guru Jan19 answered $n +1$th Fibonacci number modulo $n$ Jan4 comment Exact power of $p$ that divides the discriminant of an algebraic number field The statement will be easier to follow if you suffix the $\beta$'s. If I understand, there are $f_i$ elements in $B_i$, say $\beta_{ik}$ for $1\le k \le f_i$ and then the $n$ elements $\alpha_1,\dots,\alpha_n$ are $\alpha_{ij}\beta_{ik}$ for $1\le i\le r$, $1\le j\le e_i$ and $1\le k \le f_i$. In addition I think the $x \equiv \alpha_{ij} \pmod{Q_i^{e_i}}$ should read $x \equiv 1 \pmod{Q_i^{e_i}}$. If it is so, then the "large number $N$" means possibly: $N \ge e_i$ for every $i$ as you are then free to chose $\alpha_{ij}$ with the stronger constraint $\alpha_{ij} \equiv 0 \pmod{Q_h^N}$. Dec1 revised Galois group and the Quaternion group added 1 characters in body Dec1 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. Dec1 revised Galois group and the Quaternion group Added explanation Nov30 answered Galois group and the Quaternion group Nov10 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. Nov8 awarded Yearling Nov7 answered Cover a disk with thin rectangles