The sufficient conditions for insolvability of some Diophantine equations of $n$-th degree

Eteri Samsonadze

The sufficient conditions for insolvability of the Diophantine equation ${\sum }_{i=1}^m{x}_i^n=b{c}^n$ ($n,m\ge 2$, $b,c\in \mathbb{N}$) in nonnegative integers are obtained fo…