12:22 PM
The tag is gone - it was edited away as mentioned above.
@MartinSleziak The tag is gone - in one instance it was edited away: Measures of dependence in a maximal coupling. The other question was deleted: Unique maximal coupling with constraint.
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\begin{align} 22097 & = 19\times1163 \\ 22098 & = 2 \times 3 \times 29 \times 127 \\ 22099 & = 7 \times 7 \times 11 \times 41 \\ 22100 & = 2 \times2 \times 5 \times5 \times 13 \times 17 \\ 22101 & = 3 \times 53 \times 139 \\ 22102 & = 2 \times 43 \times 257 \\ 22103 & = 23 \times 31 \times 31 \en...

2

I am considering a problem concerning Cantor set. Let $p>3$ be a prime. Is there a way to caculate the number of $1$ in the ternary expansion of $a_p=\frac{3^{p-1}-1}{p}$ or just to decide whether $1$ appears in the ternary expansion? Any result related to this quesion is also welcome.

0

I am considering a problem concerning Cantor set. Here is my quesion: Let $N\in\mathbb{N}$. Is there any way other than direct calculation to determine whether $N$ has no "1" as digits in its ternary expansion?

3

Recall the Kato-Ponce estimate for fractional powers of the operator $J = (1-\Delta)$, $$\| J^s(fg) \|_{L^r} \lesssim \| J^s f \|_{L^{p_1}} \| g \|_{L^{q_1}} + \| J^s g \|_{L^{p_2}} \| f \|_{L^{q_2}},$$ where $\frac{1}{r} = \frac{1}{p_1} + \frac{1}{q_1} = \frac{1}{p_2} + \frac{1}{q_2}$, $1<r<\i... 1 I have a question about following argument I found in these notes on Mackey functors: (2.1) LEMMA. (page 6) Let$G$be a finite group and$J$any subgroup. Whenever$H$and$K$are subgroups of$J$, there is a pullback diagram of$G$-sets$\$ \require{AMScd} \begin{CD} \Omega @>{} >> G/K \\ @V...