Partitions into Triples with Equal Products and Families of Elliptic Curves

Ahmed El Amine Youmbai, Arman Shamsi Zargar, Maksym Voznyy

Let $S_l(M,N)$ denote a set of $\ell$ triples of positive integers having the same sum $M$ and the same product $N$. For each $2\le \ell \le 4$ we establish a connection between a…