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May
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Apr
11
comment Can someone please explain the Riemann Hypothesis to me… in English?
Can anyone provide a free link to the first linked paper?
Apr
1
comment Lucas's Cyclotomic Formula
Cool, thanks, I've missed that. So, essentially, one uses the identity $\phi_n(x^2) = \phi_n(x) \phi_n(-x)$ (valid for relevant $n$'s) and applies the Gauss identity for $\phi_n$ to get the Lucas identity (with $x^2$ in place of $x$). One needs to prove some properties of $R,S$ in Gauss identity, I might fill in the details in an answer later.
Apr
1
comment Lucas's Cyclotomic Formula
@DietrichBurde Maybe I can, but I didn't find the way. Care to elaborate?
Apr
1
asked Lucas's Cyclotomic Formula
Apr
1
answered This limit: $\lim_{n \rightarrow \infty} \sqrt [n] {nk \choose n}$.
Apr
1
revised Finding the limit of $\sqrt[n]{{kn \choose n}}$
merged 2 answers
Apr
1
answered Finding the limit of $\sqrt[n]{{kn \choose n}}$
Mar
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Mar
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Mar
9
accepted Odd-Order Groups with Cyclic p-Sylow Subgroups (for smallest p | G)
Dec
20
revised Odd-Order Groups with Cyclic p-Sylow Subgroups (for smallest p | G)
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Dec
20
comment Odd-Order Groups with Cyclic p-Sylow Subgroups (for smallest p | G)
@Timbuc I changed my wording. (BTW, $C_p \times C_p$ indeed gives a new example, yet $C_{p^2}$ is still a particular case of my example, by taking the field $\mathbb{F}_{q}$ to be a quadratic extension of a prime field.)
Dec
20
comment Odd-Order Groups with Cyclic p-Sylow Subgroups (for smallest p | G)
@Timbuc I meant "The subgroup generated by raising elements of $\mathbb{F}_{q}^{\times}$ to the $c$-power". As you said, your example can be expanded and is a generalization of my example. If no other example will be found in the next days I'll accept it as the answer, but for the mean time I'm leaving it as is.
Dec
20
comment Odd-Order Groups with Cyclic p-Sylow Subgroups (for smallest p | G)
@Myself Yes, those examples are the same. This is $G_{p,\frac{p-1}{q}}$. Can be seen by writing the group operation explicitly. In particular, this means we can't get more examples by taking non-abelian groups whose order is a product of 2 odd primes.
Dec
20
revised Odd-Order Groups with Cyclic p-Sylow Subgroups (for smallest p | G)
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Dec
20
asked Odd-Order Groups with Cyclic p-Sylow Subgroups (for smallest p | G)
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