Eteri Samsonadze

activity

20242026

collaborators

3 papers

math.NT2026

Sufficient conditions for solvability of linear Diophantine equations, and Frobenius numbers

Eteri Samsonadze

The sufficient conditions for solvability of a linear Diophantine equation $\sum_{i = 1}^{n} a_{i} x_{i} = b$ (with $a_{1}, a_{2}, ..., a_{n} \in N$ ) in non-negative integers $x_1,x_2,...,x_n…

math.NT2025

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

Eteri Samsonadze

The sufficient conditions for insolvability of the Diophantine equation $\sum_{i = 1}^{m} x_{i}^{n} = b c^{n}$ ( $n, m \geq 2$ , $b, c \in N$ ) in nonnegative integers are obtained fo…

math.GM2024

On sums of powers of natural numbers

Eteri Samsonadze

The problem of finding the sum of a polynomial's values is considered. In particular, for any $n \geq 3$ , the explicit formula for the sum of the $n$ th powers of natural numbers $S_…

Sufficient conditions for solvability of linear Diophantine equations, and Frobenius numbers

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

On sums of powers of natural numbers

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