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Putnam 1994 A4

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July 12, 2014
Putnamalgebrapolynomialquadraticscollege contests

Problem Statement

Let AA and BB be 2×22\times 2 matrices with integer entries such that A,A+B,A+2B,A+3B,A, A+B, A+2B, A+3B, and A+4BA+4B are all invertible matrices whose inverses have integer entries. Show that A+5BA+5B is invertible and that its inverse has integer entries.
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