Necessary conditions for binomial collisions

We shall give some necessary conditions for the equation $\left(\genfrac{}{}{0px}{}{x}{a}\right)=\left(\genfrac{}{}{0px}{}{y}{b}\right)$ to hold: if $\left(\genfrac{}{}{0px}{}{2n+\delta }{n-m}\right)=\left(\genfrac{}{}{0px}{}{2n+l}{n-k}\right)$ with $\delta =0$ or $1$, $0<m\leq 0.735k$,$k<n$and$n$sufficientlylarge,then$l>(cn/\log n)^{40/21}$ for some constant $c$.