Factorial Numbers and Patterns in their Prime Factors
Abstract: Factorial numbers play a fundamental role in number theory, combinatorics, and mathematical analysis. Factorial of a natural number n is the product of the first n natural numbers, factorials exhibit rich arithmetic structures, particularly in the distribution and behavior of their prime factors. This paper presents a detailed study of factorial numbers with emphasis on patterns arising in their prime factorization. Classical results such as Legendre's formula and Wilson?s theorem are discussed, along with observations on the growth of prime powers in factorials.
Keywords: Factorial numbers, prime factorization, Legendre's formula, prime powers, number theory
How to Cite?: Sajitha K M, "Factorial Numbers and Patterns in their Prime Factors", Volume 6 Issue 12, December 2017, International Journal of Science and Research (IJSR), Pages: 1996-1998, https://www.ijsr.net/getabstract.php?paperid=SR171212200243, DOI: https://dx.doi.org/10.21275/SR171212200243