2026-09-20T08:37:49Zhttps://wakespace.lib.wfu.edu/server/oai/request

oai:null:10339/593232026-09-02T11:05:53Zcom_10339_14934col_10339_38132

Southwick, Jeremiah T. 2016-05-21T08:35:53Z 2016-05-21T08:35:53Z 2016 https://wakespace.lib.wfu.edu/handle/10339/59323 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. en Wake Forest University Fibonomial Triangle Divisibility Conditions for Fibonomial Coefficients Thesis Mason, Sarah K Kirkman, Ellen Rouse, Jeremy A Mathematics open.access