Eteri Samsonadze

activity

20212025

most citedOn sums of powers of natural numbers

1 citations · 1 across the 5 of their papers we have counts for

collaborators

5 papers

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★ 1 cited

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_…

math.NT2024

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.NT2023

Formulae for the number of non-negative integer solutions of linear Diophantine equation and inequality

Eteri Samsonadze

New formulae are presented for the number $P (b)$ of non-negative integer solutions of a Diophantine equation $\sum_{i = 1}^{n} a_{i} x_{i} = b$ and for the number $Q (b)$ of non-negative inte…

math.NT2021

On the number of integer non-negative solutions of a linear Diophantine equation

Eteri Samsonadze

We deal with the problem to find the number $P (b)$ of integer non-negative solutions of an equation $\sum_{i = 1}^{n} a_{i} x_{i} = b$ , where $a_{1}, a_{2}, ..., a_{n}$ are natural numbers and $b$ …

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

On sums of powers of natural numbers

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

Formulae for the number of non-negative integer solutions of linear Diophantine equation and inequality

On the number of integer non-negative solutions of a linear Diophantine equation

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