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pro vyhledávání: '"Samsonadze, Eteri"'
Autor:
Samsonadze, Eteri
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 $S_n=\sum_{x=1}^{m}x^{n}$ is proved: $$\sum_{x=1}^{m}x^{n}=(-1)^{n}m(m+1)
Externí odkaz:
http://arxiv.org/abs/2411.11859
Autor:
Samsonadze, Eteri
A linear Diophantine equation $\sum_{i=1}^{n}a_ix_i=b$ is considered, where $a_1,a_2,...,a_n$ are coprime natural numbers, $b$ is an non-negative integer, $x_i$ $(i=1,2,...,n)$ are non-negative integers. It is proved that if $\left[\frac{b}{M}\right]
Externí odkaz:
http://arxiv.org/abs/2408.17266
Autor:
Samsonadze, Eteri
Publikováno v:
Proc. Tbilisi State University, 239 (1983), 36-42
New formulae are presented for the number $P(b)$ of non-negative integer solutions of a Diophantine equation $\sum_{i=1}^{n}a_ix_i=b$ and for the number $Q(b)$ of non-negative integer solutions of the Diophantine inequality $\sum_{i=1}^{n}a_ix_i\leq
Externí odkaz:
http://arxiv.org/abs/2310.17382
Autor:
Samsonadze, Eteri
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 $b$ is a non-negative integer. As different from the traditional methods o
Externí odkaz:
http://arxiv.org/abs/2108.04756