- #1
Ackbach
Gold Member
MHB
- 4,155
- 91
Here is this week's POTW:
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For $n\ge 1$, let $d_n$ be the greatest common divisor of the entries of $A^n-I$, where
$$A=\begin{bmatrix}3&2\\4&3\end{bmatrix} \qquad \text{and} \qquad
I=\begin{bmatrix}1&0\\0&1\end{bmatrix}.$$
Show that $\displaystyle \lim_{n\to\infty}d_n=\infty$.
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!
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For $n\ge 1$, let $d_n$ be the greatest common divisor of the entries of $A^n-I$, where
$$A=\begin{bmatrix}3&2\\4&3\end{bmatrix} \qquad \text{and} \qquad
I=\begin{bmatrix}1&0\\0&1\end{bmatrix}.$$
Show that $\displaystyle \lim_{n\to\infty}d_n=\infty$.
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Remember to read the http://www.mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to http://www.mathhelpboards.com/forms.php?do=form&fid=2!