A tangent inequality over primes

S. I.  Dimitrov

doi:10.37863/umzh.v75i7.7184

S. I. Dimitrov Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Bulgaria

DOI: https://doi.org/10.37863/umzh.v75i7.7184

Анотація

УДК 511

Дотична нерівність над простими числами

Введено нову діофантову нерівність з простими числами. Нехай $1<c<\dfrac{10}{9}.$ Показано, що для довільного фіксованого $\theta>1,$ кожного достатньо великого додатного числа $N$ та малого сталого числа $\varepsilon>0$ дотична нерівність \begin{equation*} \big|p^c_1\tan^\theta(\log p_1)+ p^c_2\tan^\theta(\log p_2)+ p^c_3\tan^\theta(\log p_3) -N\big|<\varepsilon \end{equation*} має розв'язок у простих числах $p_1,$ $p_2$ та $p_3.$

Посилання

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