Title | Representation of natural numbers by sum of four squares of almost-prive having a special form |

Publication Type | Journal Article |

Year of Publication | 2020 |

Authors | Petrov ZH, Todorova TL |

Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |

Volume | 107 |

Start Page | 15 |

Pagination | 15-29 |

ISSN | 1313-9215 (Print) 2603-5529 (Online) |

Keywords | almost-primes, Lagrange's equation, quadratic irrational numbers |

Abstract | In this paper we consider the equation $x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2} = N$, where $N$ is a sufficiently large integer and prove that if $\eta $ is quadratic irrational number and $0 < \lambda < \frac{1}{10}$, then it has a solution in almost-prime numbers $x_{1}, \ldots , x_{4}$, such that $\{ \eta x_{i} \} < N^{-\lambda }$ for $i = 1, \ldots , 4$. |

DOI | 10.60063/GSU.FMI.107.15-29 |

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107-15-29.pdf | 397.76 KB |