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

Eteri Samsonadze

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arXiv · 2310.17382

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

Eteri Samsonadze

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Abstract

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 $\sum_{i=1}^{n}a_ix_i\leq b$ $(a_i>0, b\geq 0$).

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Eteri Samsonadze. 2023-10-26. Formulae for the number of non-negative integer solutions of linear Diophantine equation and inequality. https://arxiv.org/abs/2310.17382

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