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comment For what values of $a, n$ the number $2^a\cdot 3^n+1$ is prime?
@DietrichBurde So is there any site where if I put a list of values of $n$, we shall get which $2^a3^n+1$ will be prime when $a$ is given?
Feb
10
comment For what values of $a, n$ the number $2^a\cdot 3^n+1$ is prime?
Thank you. Suppose I want to check for $a=2$, $n=1,2,3,\cdots, 100$ how to do that ?
Feb
10
asked For what values of $a, n$ the number $2^a\cdot 3^n+1$ is prime?
Feb
4
asked what can we say about $\varphi^{-1}(2^a), \varphi^{-1}(2^\alpha), \varphi^{-1}(2^\beta)$ where $a=\alpha+\beta$?
Jan
27
comment Could you solve $x↑^n2=x↑^m2$?
What is W here ?
Jan
21
revised Determine values of k for a matrix to have a unique solution
$M =\left[ \begin{array}{cc} k^3 + 3k & k+5 & k+3 & k^5+(k+3)^2 \\ 0 & k & 1 & 3 \\ 0 & 0 & k^3+k^2-6k & k(k^2-9)\\ \end{array}\right]$
Jan
21
suggested approved edit on Determine values of k for a matrix to have a unique solution
Jan
19
revised Show that $rank(A) \ngeq \frac{[tr(A)]^2 }{tr(A^2)}$
$rank(A) \ngeq \frac{[tr(A)]^2 }{tr(A^2)}$
Jan
19
revised Find the nth power of a matrix
Added two tags
Jan
19
suggested approved edit on Find the nth power of a matrix
Jan
19
suggested approved edit on Show that $rank(A) \ngeq \frac{[tr(A)]^2 }{tr(A^2)}$
Jan
9
awarded  Nice Question
Jan
9
accepted How to find $f$ and $g$ if $f\circ g$ and $g\circ f$ are given?
Dec
16
comment What can we say about $D_{2n}$ and $D_n$ if $n$ is even?
So in that case, can we bring some isomorphism relation between $D_{2n}$ and $D_n$ through the direct product or some thing like that? Just similar to odd $n$ case ?
Dec
16
comment What can we say about $D_{2n}$ and $D_n$ if $n$ is even?
No problem. I meant to say this $D_m:=\langle r, f\rangle =\{ r, f : r^m = f^2 = (rf)^2 =e \}$
Dec
16
comment What can we say about $D_{2n}$ and $D_n$ if $n$ is even?
Well, if $n$ is odd, then the relation is already there. For even, I think there should be some subgroup of $D_{2n}$ to be isomorphic to $D_n$. But no idea what else should I approach. :-(
Dec
16
asked What can we say about $D_{2n}$ and $D_n$ if $n$ is even?
Dec
4
comment How to show $\frac{\mathbb{Z}_m\times \mathbb{Z}_n}{\langle (a,b)\rangle}\simeq \mathbb{Z}_{\frac mc}\times \mathbb{Z}_{\frac nd}$?
Thank you so much for your beautiful answer. It was really nice explanation. Would you please reply what is SNF ? The line "By using the SNF for the matrix whose rows are (a,b), (m,0), and (0,n) one find...." was not clear to me. :-(
Dec
4
comment How to show $\frac{\mathbb{Z}_m\times \mathbb{Z}_n}{\langle (a,b)\rangle}\simeq \mathbb{Z}_{\frac mc}\times \mathbb{Z}_{\frac nd}$?
@user26857 Many many thanks to you for your reply. I understood my fault. I knew $c, d$ will be relatively prime which I showed in my attempt but forgot to mention in the question. Sorry for that.
Dec
4
comment How to show $\frac{\mathbb{Z}_m\times \mathbb{Z}_n}{\langle (a,b)\rangle}\simeq \mathbb{Z}_{\frac mc}\times \mathbb{Z}_{\frac nd}$?
Compare to you, my knowledge is definitely less and so I am sorry that I made mistake. Thank you for your correction. There are indeed several choice for $c, d$ but my intention was for just a suitable choice. Although I failed to make the appropriate question format. Extremely Sorry for that. between did you mean $\mathbb{Z}_4\oplus \mathbb{Z}_1$ as external direct product ? Cause I learnt from MSE that people use $\times $ to denote the same. For finite case of direct product, one can use $\oplus $ symbol. I hope you meant that.