A quinary diophantine inequality by primes with one of the form $\mathbf{p=x^2+y^2+1}$

S. I. Dimitrov

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arXiv · 2107.04028

A quinary diophantine inequality by primes with one of the form $\mathbf{p=x^2+y^2+1}$

S. I. Dimitrov

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Abstract

In this paper we show that, for any fixed $1 0$, the diophantine inequality \begin{equation*} |p_1^c+p_2^c+p_3^c+p_4^c+p_5^c-N|<\varepsilon \end{equation*} has a solution in prime numbers $p_1,\,p_2,\,p_3,\,p_4,\,p_5$, such that $p_1=x^2 + y^2 +1$.

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BibTeX RIS

S. I. Dimitrov. 2021-06-29. A quinary diophantine inequality by primes with one of the form $\mathbf{p=x^2+y^2+1}$. https://arxiv.org/abs/2107.04028

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