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Putnam 1994 B4

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July 12, 2014
Putnamlinear algebramatrixlimitinductioncollege contests

Problem Statement

For n≥1n\ge 1 let dnd_n be the gcd⁡\gcd of the entries of An−I2A^n-\mathcal{I}_2 where A=\begin{pmatrix} 3&2\\ 4&3\end{pmatrix}  \text{ and }  \mathcal{I}_2=\begin{pmatrix}1&0\\ 0&1\\\end{pmatrix} Show that lim⁡n→∞dn=∞\lim_{n\to \infty}d_n=\infty.
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