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Putnam 2015 B3

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December 6, 2015
PutnamPutnam 2015Putnam matrices

Problem Statement

Let SS be the set of all 2×22\times 2 real matrices M=(abcd)M=\begin{pmatrix}a&b\\c&d\end{pmatrix} whose entries a,b,c,da,b,c,d (in that order) form an arithmetic progression. Find all matrices MM in SS for which there is some integer k>1k>1 such that MkM^k is also in S.S.
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