Hey Zaid. This book tells you all there is to know about 'how to solve hypergeometric series'. A = B: Marko Petkovsek, Herbert S Wilf, Doron Zeilberger: 9781568810638: Amazon.com: BooksZaidAlyafey said:I came across the interesting Kummer's Theorem .Does anybody know an elementary proof ?
Kummer's Theorem is a mathematical theorem that states that for any positive integers m and n, the binomial coefficient (m choose n) is divisible by p, where p is a prime number, if and only if the base p representation of n has no carries when added to the base p representation of m.
Kummer's Theorem was discovered by German mathematician Ernst Kummer in the 19th century.
Kummer's Theorem has significant applications in number theory, algebra, and combinatorics. It has also been used to prove other mathematical theorems and has been a subject of study in its own right.
An elementary proof of Kummer's Theorem uses basic mathematical concepts and does not require advanced mathematical techniques. It is a more accessible and intuitive way of understanding the theorem.
Yes, there is a generalized version of Kummer's Theorem known as the Lucas-Kummer Theorem, which applies to any positive integer base. This theorem was also developed by Kummer and French mathematician Édouard Lucas.