Matrix Powers of Column-Justified Pascal Triangles and Fibonacci Sequences
Abstract
If L, respectively R are matrices with entries binomi-1,j-1, respectively binomi-1,n-j, it is known that L2 = I (mod 2), respectively R3 = I (mod 2), where I is the identity matrix of dimension n > 1 (see P10735-May 1999 issue of the American Mathematical Monthly). We generalize it for any prime p, and give a beautiful connection to Fibonacci numbers.
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