Various Problems Concerning Factorials, Binomial Coefficients, Fibonomial Coefficients, and Palindromes

Abstract

In this thesis, we study on various problems concerning factorials, bonomial coefficients, Fibonomial coefficients, and palindrome. We calculate the p-adic valuations of certain factorials and apply them to express the p-adic valuations of Fibonomial coefficient in terms of the p-adic valuations of some binomial coefficients. This lead us to obtain explicit formula for the p-adic valuations of Fibonomial coefficients and the related divisibility of Fibonomial coefficients. In addition, we also evaluate a upper bounds, lower bounds, and asymptotic formulas for reciprocal sum of palindromes.

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