On the Diophantine equation $\left(\genfrac{}{}{0ex}{}{n}{k}\right)=\left(\genfrac{}{}{0ex}{}{m}{l}\right)+d$

Homero R. Gallegos-Ruiz, Nikolaos Katsipis, Szabolcs Tengely +1

By finding all integral points on certain elliptic and hyperelliptic curves we completely solve the Diophantine equation $\left(\genfrac{}{}{0ex}{}{n}{k}\right)=\left(\genfrac{}{}{0ex}{}{m}{l}\right)+d$ for $-3\le d\le 3$ and $(k,…