Solvability of $\left(\genfrac{}{}{0ex}{}{2k}{k}\right)=\left(\genfrac{}{}{0ex}{}{2a}{a}\right)\left(\genfrac{}{}{0ex}{}{x+2b}{b}\right)$

Meaghan Allen

Suppose $k,x,$ and $b$ are positive integers, and $a$ is a nonnegative integer such that $k=a+b$. In this paper, we will prove $\left(\genfrac{}{}{0ex}{}{2k}{k}\right)=\left(\genfrac{}{}{0ex}{}{2a}{a}\right)\left(\genfrac{}{}{0ex}{}{x+2b}{b}\right)$ if an…