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Dec
22
awarded  Revival
Dec
22
answered Generalizing Ramanujan's proof of Bertrand's Postulate: Can Ramanujan's approach be used to show a prime between $4x$ and $5x$ for $x \ge 3$
Dec
18
awarded  Nice Question
Nov
8
awarded  Yearling
Jun
21
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.
Jun
21
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
Jun
21
answered How prove that:$\varphi(2)+\varphi(3)+\varphi(4)+\cdots+\varphi(n)\ge\frac{n(n-1)}{4}+1$
Jun
4
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 $S(L,t) = n(n+1)(2n+1)/6 + S(t,b)$.
May
4
comment Do these inequalities regarding the gamma function and factorials work?
Is $x$ an integer? if not what does it mean $n \vert (x+1)$?
Apr
2
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)
Mar
9
awarded  Guru
Jan
19
answered $n +1$th Fibonacci number modulo $n$
Jan
4
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 $\alpha_{ij} \equiv 0 \pmod{Q_h^N}$.
Dec
1
revised Galois group and the Quaternion group
added 1 characters in body
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