Diophantus Equations and Partially Ordered Sets

Addea Gupta

In [1] it is shown that the Diophantine equation $(k!{)}^n+k^n=(n!{)}^k+n^k$ only has the trivial solution $n=k$, and $(k!{)}^n-k^n=(n!{)}^k-n^k$ only has the solutions $n=k$, $(n, k)=(1,…