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Golden Matrix Ring Mod \(p\)

by Kung-Wei Yang (Western Michigan University)

This article originally appeared in:
Mathematics Magazine
June, 2008

Subject classification(s): Geometry and Topology | Plane Geometry
Applicable Course(s): 4.3 Number Theory

The author uses the golden matrix ring \(Z(A)\) generated by \(A= \left[ \begin{array}{cccc} 0 & 1 \\ 1 & 1 \end{array} \right] \) to prove certain identities involving Fibonacci numbers. In particular, he shows that every prime divides some (and hence infinitely many) Fibonacci numbers, and also verifies some generalizations and extensions of such results.

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Capsule Course Topic(s):
Number Theory | Congruences
Number Theory | Number Sequences
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