Anjan3
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 2d 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.