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Divisibility Conditions for Fibonomial Coefficients

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title
Divisibility Conditions for Fibonomial Coefficients
author
Southwick, Jeremiah T.
abstract
The fibonomial triangle has been shown by Chen and Sagan to have a fractal nature mod 2 and 3. Both these primes have the property that the Fibonacci entry point of $p$ is $p+1$. We study the fibonomial triangle mod 5, showing with a theorem of Knuth and Wilf that the triangle has a recurring structure under divisibility by five. While this result is not new, our method of proof is new and suggests a theorem relating the divisibility by a general prime $p$ of a fibonomial coefficient to the divisibility by $p$ of a product of fibonomial coefficients in the first $p$ rows of the fibonomial triangle. This product is constructed using a particular base. We give necessary and sufficient conditions for which primes $p$ satisfy the theorem, namely that the Fibonacci entry point of $p$ must be greater than or equal to $p$ for the theorem to hold. Lastly, we conclude with a discussion concerning further directions of research.
subject
Fibonomial
Triangle
contributor
Mason, Sarah K (committee chair)
Kirkman, Ellen (committee member)
Rouse, Jeremy A (committee member)
date
2016-05-21T08:35:53Z (accessioned)
2016-05-21T08:35:53Z (available)
2016 (issued)
degree
Mathematics (discipline)
identifier
http://hdl.handle.net/10339/59323 (uri)
language
en (iso)
publisher
Wake Forest University
type
Thesis

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