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Golden Matrix Ring Mod \(p\)

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.

Old Node ID: 
3689
MSC Codes: 
97G40
Author(s): 
Kung-Wei Yang (Western Michigan University)
Publication Date: 
Monday, June 20, 2011
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
June, 2008
Subject(s): 
Geometry and Topology
Plane Geometry
Topic(s): 
Congruences
Number Sequences
Flag for Digital Object Identifier: 
Publish Page: 
Furnished by JSTOR: 
File Content: 
Rating Count: 
5.00
Rating Sum: 
15.00
Rating Average: 
3.00
Applicable Course(s): 
4.3 Number Theory
Modify Date: 
Saturday, August 25, 2012
Average: 3 (5 votes)

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