Title | ON AN EQUATION INVOLVING FRACTIONAL POWERS WITH PRIME NUMBERS OF A SPECIAL TYPE |

Publication Type | Journal Article |

Year of Publication | 2017 |

Authors | Petrov Z |

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

Volume | 104 |

Pagination | 171-183 |

ISSN | 0205-0808 |

Keywords | sieve methods, Waring’s problem |

Abstract | We consider the equation $[p^c_1]+[p^c_2]+[p^c_3] = N$, where $N$ is a sufficiently large integer, and $[t]$ denotes the integer part of $t$. We prove that if $1 < c < \frac{17}{16}$, then it has a solution in prime numbers $p_1, p_2, p_3$ such that each of the numbers $p_1 + 2, p_2 + 2, p_3 + 2$ has at most $\Big[\frac{95}{17−16c}\Big]$ prime factors, counted with their multiplicities. |

2000 MSC | 11P05 (Primary); 11N36 (Secondary) |

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104-171-183.pdf | 169.45 KB |