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

 Заглавие Representation of natural numbers by sum of four squares of almost-prive having a special form Вид публикация Journal Article Година на публикуване 2020 Автори Petrov ZH, Todorova TL Списание Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique Том 107 Start Page 15 Pagination 15-29 ISSN 1313-9215 (Print) 2603-5529 (Online) ключови думи almost-primes, Lagrange's equation, quadratic irrational numbers Резюме 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 $i = 1, \ldots , 4$.
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