(Suleyman Demirel University, 2008) Selim Guvercin
This project explores several interesting and useful features of binomial coefficients. The work focuses on understanding when certain binomial numbers are odd or even, how they behave with respect to prime numbers, and whether some of them can form simple number patterns. The project also shows a clear connection between binomial coefficients and prime numbers by proving that one well-known property of these coefficients works only for primes. The study is divided into two parts: the first part introduces the basic concepts needed for the results, and the second part provides explanations for the main findings. Overall, the project offers a clearer understanding of how binomial coefficients behave and why these properties are important in basic mathematics.