Continuum cardinality of the set of solutions of one class of equations that contain the function of frequency of ternary digits of a number

• Дата: 2008
• Автори: Kotova, O. V., Котова, О. В.
• Формат: Стаття
• Мова: Українська; Англійська
• Опубліковано: Institute of Mathematics, NAS of Ukraine 2008
• Онлайн доступ: https://umj.imath.kiev.ua/index.php/umj/article/view/3255
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We study the equation v1 (x) = x, where v1 (x) is the function of frequency of the digit 1 in ternary expansion of x. We prove that this equation has a unique rational solution and a continuum set of irrational solutions. An algorithm for the construction of solutions is proposed. We also describ...